Olimpiade Math SD
Pecahan, Persen dan Rasio
: 1. Compute the sum of a, b and c given that and the product of a, b and c is 1920. (PMWC 9th Team)
: 2. Find the fraction with the smallest denominator between 97/36 and 96/35. (PMWC 7th Individual)
On what letter in the following figure the number 1/5 lies exactly? (OSN SD Uraian 2012)
There are nine fractions between 1/5 and 1/2 such that the difference between any two successive fractions is constant. Find the sum of these eleven fractions. (PMWC 8th Team)
Evaluate 2014×(1/962+2/45)+1969×(1/2014-2/45)+45×(1/2014-2/962). (NMOS 2014)
Given that x and y are whole numbers such that 1/x-1/y=1/6, find the largest value of
x+y. (NMOS 2014 Special Round)
Find the value of (101 + 103 + 105 + … + 197 + 199)/(1 + 3 + 5 + … + 97 + 99). (NMOS 2011 Special Round)
A sequence of 20 numbers is given as follows.
(4/5+5/25),(4/6+6/25),(4/7+7/25),…,(4/23+23/25),(4/24+24/25)
It is known that each of the numbers is of the form (4/k+k/25), where k=5,6,…,24.
Given that m/n is the smallest value among the 20 numbers in the sequence and that m/n is in its simplest form, determine the value of m+n. (NMOS 2014 Special Round)
The decimal form of 3/32 is 0, 09375. The decimal form of 29/32 is … (OSN SD Isian Singkat 2012)
Given that x/9900=0.201414141414…, a repeated decimal where ‘14’ keeps repeating, find the value of the whole number x. (NMOS 2014 Special Round)
Let a = 0.363636… and b = 0.515. Find the digit on the 2011th decimal place of the product ab. (IMSO 2011 Essay Problem)
What is the largest value of positive integer n such that n/666=0.2y17y17y17⋯, where y is a single digit and y17 is repeating? (PMWC 20th Individual)
The positive integers a and b are such that 5/7<a/b<9/11. Find the value of a+b when b takes the smallest possible value. (IMSO 2012 Short Answer)
The extended fraction
1/(3+1/(3+1/(3+1/3)))
Can be expressed as a simple fraction 33/A. Find the value of A. (NMOS 2015)
Let a,b dan c are natural numbers such that a/2+b/5+c/7=69/70. The result of 2a+5b+7c is … (OSN SD Isian Singkat 2018)
Find the value of
(2009/2010+2010/2011+6/7)(1/2+2009/2010+2010/2011+2/5)-(1/2+2009/2010+2010/2011+6/7)(2009/2010+2010/2011+2/5)
(IMSO 2011 Short Answer)
Study the following pattern.
1/(1×2)=1/2,1/(1×2)+1/(2×3)=2/3,1/(1×2)+1/(2×3)+1/(3×4)=3/4.
Given that 1/(1 × 2)+1/(2 × 3)+1/(3 × 4)+⋯+1/(2013 × 2014)=(a + 2)/(a + 3), where a is a positive integer. Find the value of a. (IMSO 2013 Short Answer)
Find x if
x/(1×2×3)+x/(2×3×4)+x/(3×4×5)+⋯+x/(8×9×10)=11.
(PMWC 16th Team)
Replace the letters a, b, c and d in the following expression with the numbers 1, 2, 3 and 4, without repetition:
a+1/(b+1/(c+1/d))
Find the difference between the maximum value and the minimum value of the expression. (PMWC 9th Team)
Find the greatest value of a+1/(b + 1/c)+d+1/(e + 1/f)+g+1/(h + 1/i) where each letter represents a different non-zero digit. (PMWC 12th Individual)
Note that 1+ 1/(1+1/(2+1/4))=1+1/(1+4/9)=1+9/13=22/13. It is known that the fraction 13/10 can be written as 1+1/(a+1/(b+1/c)), where a,b and c are whole numbers. Find the value of a+2b+3c.
(NMOS 2013 Special Round)
AXXX and XXXB are two four-digit numbers, where A,B and X are all distinct. If AXXX/XXXB=2/5, find A,B and X. (PMWC 3rd Individual)
The fraction 44/37 can be written in the form of 1+1/(x + 1/(y + 1/z)), where x,y and z are distinct integers. Find the value of x+y+z. (PMWC 3rd Team)
Let A=x+1/(y+1/z), B= y+1/(z+1/x), C=z+1/(x+1/y), where x,y and z are positive integers. If A=37/16, calculate the value of A×B×C. (PMWC 15th Team)
What is the 2013th term in the sequence 1/1, 2/1, 1/2, 3/1, 2/2, 1/3, 4/1, 3/2, 2/3, 1/4,… ? (PMWC 16th Individual)
What is the largest integer less than or equal to the expression (IMSO 2015 Essay Problem)
1/(1/1985+1/1986+1/1987+⋯+1/2015)
Find the last digit of N, where
N=(1+2+3+4)+(1^2+2^2+3^2+4^2 )+⋯+(1^2012+2^2012+3^2012+4^2012 ).
(PMWC 15th Individual)
There are positive integers k,n,m such that 19/20<1/k+1/n+1/m<1. What is the smallest possible value of k+n+m? (PMWC 4th Team)
Let a,b and c be different positive integers such that 1=1/2+1/3+1/7+1/a+1/b+1/c. What is the smallest possible value of a+b+c? (IMSO 2015 Essay Problem) ?
Diketahui lima pecahan 1/3,1/6,1/9,1/12 dan 1/15. Empat dari lima pecahan tersebut dilambangkan dengan huruf a,b,c dan d. Jika a+b+c=7/12 dan c×d=1/45 maka nilai d= … (OSN SD Isian Singkat 2016)
Whenever Sam reads a date like 20/11/2016, he incorrectly interprets it as two divisions, with the second one evaluated before the first one:
20÷(11÷2016)=40320/11=3665 5/11
For some dates, like this one, he does not get an integer, while for others, like 20/8/2016, he gets 20÷(8÷2016)=5040 , an integer. How many dates this year (day/month/year) give him a non-integer? (IMSO 2016 Short Answer)
Penjumlahan pecahan di antara empat pecahan 1/3, 1/9,1/27, dan 1/81 menghasilkan berbagai bilangan. Sebagai contoh bilangan 4/9 dapat diperoleh dengan menjumlahkan dua pecahan, yaitu 1/3+1/9, atau empat pecahan 1/9+1/9+1/9+1/9 . Bilangan 70/81 dapat diperoleh dengan menjumlahkan paling sedikit . . . pecahan. (OSN SD Isian Singkat 2015)
We insert +,-,× and ÷ each exactly once into the following four boxes, (1/2□1/9), (1/3□1/8),(1/4□1/7), (1/5□1/6) so that the sum of these four terms is the largest. In this case, if the second largest among these four terms is written as A/B in its simplest form, find A+B. (NMOS 2012 Special Round)
In the expression a/b+ c/d+ e/f, each letter is replaced by a different digit among 1, 2, 3,
4, 5, and 6. What is the smallest possible value of this expression? (IMSO 2007 Short Answer)
Let ∎ and ∆ be two distinct positive integers such that ∎-∆=2013, ∎/∆=(∎ - ∆ - 669)/(∎ - ∆ - 2011). What is the value of ∎? (IMSO 2012 Short Answer)
The sum of the reciprocals of four positive integers a,b,c and d (not necessarily different) is 7/10, i.e. 1/a+1/b+1/c+1/d=7/10. What is the smallest possible sum of these four integers? (PMWC 17th Individual)
Given that 1+1/2^2 +1/3^2 +⋯=M, and 1+1/3^2 +1/5^2 +⋯=K, find the ratio of M∶K.
(PMWC 16th Individual)
In an examination, students can obtain 4 possible grades: A,B,C and D. 1/7 of the students got A, 1/3 of them got B, and 1/2 of them got C. If there are less than 50 students taking the examination, how many students got D? (NMOS 2006)
A huge bowl contains many sweets. On the first day, Kenneth ate 1/7 of the number of sweets. On the second day, he ate 1/6 of the remaining number of sweets. On the third day, he ate 1/5 of the remaining number of sweets. On the fourth day, he ate 1/4 of the remaining number of sweets. How many sweets were there in the bowl initially if there are 6 sweets remaining after the fourth day? (NMOS 2007)
Wayne has 7/13 of the number of stamps that Monica has. After Peter gave an equal number of stamps to Wayne and Monica, Wayne has 9/10 of the number of stamps that Monica has. If the number of stamps Peter gave to Wayne is between 500 and 550, what is the number of stamps that Peter gave to Monica? (NMOS 2009 Special Round)
The amount of money David has is 1/4 of the amount of money Samuel has. If Samuel gives David $500, Samuel will have 2/3 of the amount of money David has. How much money do they have altogether? (NMOS 2010)
At a wedding dinner, all the men wear pants. 1/4 of the number of women wear pants while the rest of the women dresses. If the number of women is 2/3 of the number of men, what percentage of the people at the wedding dresses? (NMOS 2010)
Di kotak terdapat sejumlah bola merah, hijau, dan biru. Banyaknya bola merah dan biru di kotak tersebut berturut-turut adalah 1/4 bagian dan 2/5 bagian. Banyaknya bola hijau sama dengan dua kali banyaknya bola merah dikurangi 9. Banyaknya bola hijau di kotak tersebut adalah . . . . (OSN SD Isian Singkat 2011)
Sejumlah salak yang berbobot sama dimasukkan ke dalam sebuah keranjang. Apabila diambil 1/4 bagian dari isi keranjang, berat keranjang beserta salak yang tersisa turun menjadi 19, 5 kg. Namun apabila yang diambil hanya 1/6 bagian dari isi keranjang, berat keranjang beserta salak yang tersisa hanya turun menjadi 21, 5 kg. Berapa berat keranjang beserta salak sisanya apabila diambil 2/3 bagian dari salak? (OSN SD Uraian 2011)
Pada hari lebaran, Pak Samsul ingin membagikan sejumlah uang kepada cucu-cucunya. Pak Samsul membagi cucu-cucunya ke dalam beberapa kategori, yaitu usia TK, SD, SMP dan SMA. Dari sejumlah uang yang disiapkan, 2/5 -nya untuk usia TK, 1/5 -nya untuk usia SD, dan 1/3-nya untuk usia SMP, dan sisanya untuk usia SMA. Bagian untuk usia SMA adalah . . . bagian. (OSN SD Isian Singkat 2012)
Linda has 2 containers, Container A and Container B. The amount of water in Container A is 4/5 of the amount in Container B at first. When 200 ml of water from Container A is poured into Container B, the amount of water in Container A is 1/2 the amount in Container B. How much water was in Container A at first? (NMOS 2006)
Melvin, Nelson and Oliver were playing cards.
At first, Melvin started with 40 cards and then he gained 5/8 more than his original number of cards from Nelson.
In the next round, Melvin and Nelson each lost 1/4 of Melvin’s original number of cards to Oliver.
In the final round, Melvin gained 1/8 of his original number of cards from Nelson.
After the final round, Melvin, Nelson and Oliver all have the same number of cards.
What was the total number of cards Melvin, Nelson and Oliver had at first? (NMOS 2007)
A piece of square paper, B, is cut from a big piece of square paper , A, such that its side is 1/2 that of the side of A. Another smaller square piece of paper, C, is cut from B such that its side 2/3 that of the side of B. The area of C is Δ/ of the area of A, where Δ and are whole numbers. Find the smallest value of Δ+ . (NMOS 2007)
In a class of 45 students, 6 girls and 1/7 of the boys took part in a Mathematics competition. There are an equal number of girls and boys who did not take part in this competition. Find the number of girls in the class. (NMOS 2008 Special Round)
Aaron, Betty, Calvin, Diana and Edward ate 21 cakes altogether. They took turns to eat their share. After each of them finished their share, they told the group how much they had eaten. You are not told who ate the cakes first, but you are told what they had said.
Aaron said: “I have eaten 2/3 of the remaining.”
Betty said: “I have eaten half of the remaining.”
Calvin said: “I have eaten half of the remaining.”
Diana said: “I have eaten all of the remaining.”
Edward said: “The numbers of cake eaten by us are all different whole numbers.”
What is the number of cakes Edward has eaten? (NMOS 2014)
In a specific math Olympiad training class, the proportion of female students is more than 4/15, but less than 3/10, what is the smallest possible number of pupils in the class? (NMOS 2015 Special Round)
Jika 15% dari 4/5 uang Rani adalah Rp 45.000.00, maka 5/6 uang Rani adalah… (OSN SD Isian Singkat 2016)
Banyaknya bilangan pecahan a/b yang nilainya kurang dari 4 dengan pembilang dan penyebut bilangan 1, 2, 3, 4, 5 adalah (OSN SD Isian Singkat 2017)
Misalkan a,b,c dan d adalah bilangan berbeda yang dapat diganti dengan 1, 2, 3, 4 dan 5, sehingga hasil operasi a/1+b/10+c/100+d/1000 dapat diurutkan dari terkecil sampai terbesar. Berapakah hasil operasi bilangan tersebut pada urutan ke-32? (OSN SD Uraian 2018)
In the fraction a/b,a and b are positive integers. Amanda multiplied the numerator of this fraction by 340. Which positive integer closest to 2017 should Amanda add to the denominator to obtain the fraction 2a/3b ? (PMWC 20th Individual)
The fraction 221/210 is obtained as a sum of three positive fractions each less than 1 with single digit denominators. Find the largest (greatest) of these fractions in simplest form. (PMWC 21th Individual)
In a classroom, 1/4 of the pupils are girls. After 10 boys leave the room, the portion of the girls in the room becomes 1/3. What is the total number of pupils before the 10 boys leave? (IMSO 2004 Essay Problem)
The income of a taxi driver is the sum of the regular salary and some tips. The tips are 5/4 of his salary. What is the fraction of his income which comes from his tips? (IMSO 2014 Short Answer)
Unit fractions are those fractions whose numerator is 1 and denominator is any positive integer. Express the number 1 as the sum of seven different unit fractions, given five of them are 1/3,1/5,1/9,1/15 and 1/30. Find the product of the two remaining unit fractions. (IMSO 2015 Short Answer)
Class A and Class B have the same number of students.
The number of students in class A who took part in a mathematics competition is 1/3 of the students in class B who did not take part.
The number of students in class B who took part in a mathematics competition is 1/5 of the students in class A who did not take part.
Find the ratio of the number of students in class A who did not take part in this competition to the number of students in class B who did not take part. (IMSO 2016 Short Answer)
What number should be subtracted from the numerator of the fraction 537/463 and added to the denominator so that the resulting fraction is equal to 1/9? (IMSO 2017 Short Answer)
The digits 0 to 9 without repetition form two 5-digit numbers M and N. Given that M/N equals to 1/2, find the largest possible sum of M and N. (PMWC 4th Team)
Three persons together own a pile of about 200 gold coins. They originally posses 1/2 , 1/3, and 1/6 of the coins, respectively. Now each person is going to take out some coins from the pile until there is nothing left. Then the first person is to return 1/2 of what he has taken out, the second person 1/3 of what he had taken, and third person 1/6 of what he had taken. If the returned coins are equally distributed to the three persons, than each person will get back the same number of coins which he originally possessed. How many gold coins were there originally? (PMWC 5th Team)
Let 1/a+1/b+1/c=1/2005, where a and b are different four-digit positive integers (natural numbers) and c is a five-digit positive integer (natural number). What is the number c ? (PMWC 9th Individual)
Let x be a fraction between 36/35 and 183/91. If the denominator of x is 455 and the numerator and denominator have no common factor except 1, how many possible values are there for x? (PMWC 9th Individual)
Elvis has many identical pizzas. He gives 1/3 of his pizzas plus 2/3 of a pizza to Adam. He then gives 1/4 of the remaining pizzas plus half a pizza to Benny. He gives half of the remaining pizzas to Clinton. Lastly, he gives half of the remaining pizzas plus half a pizza to Deon. In the end, Elvis is left with 5 pizzas. How many pizzas does Elvis have originally? (PMWC 13th Individual)
There are three boxes of marbles. Each box contains a different number of marbles. From the first box, I remove 1/3 of the number of marbles, from the second box, I remove 1/4 of the number of marbles and from the third box, I remove 1/5 of the number of marbles. Finally, there is an equal number of marbles remaining in all the three boxes. What is the smallest possible number of marbles which I may have removed in total? (PMWC 14th Individual) There are only white and red balls in a bag. Tom takes one ball, looks in the bag and says “ 5/7 of the remaining balls are white”. After that he puts the ball back into the bag. Then Masha takes one of the balls, looks in the bag and says “ 12/17 of the remaining balls are white”. How many balls in total were there in the bag initially? (PMWC 15th Individual)
Frank had a total of 424 local and foreign stamps. He gave away 40% of the local stamps and 5/6 of the foreign stamps to his friends. Then he bought 28 foreign stamps. As a result, the number of foreign stamps he had was 16 2/3% of the number of local stamps left. How many local stamps did have at first? (NMOS 2016 Special Round)
Pak Abun menjual dua buah rumah yang masing-masing harganya Rp52.000.000,00. Ia memperoleh keuntungan 30% dari rumah pertama, tetapi menderita kerugian 20% dari rumah kedua. Ternyata secara keseluruhan Pak Abun mengalami kerugian. Berapa rupiahkah kerugiannya? (OSN SD Isian Singkat 2003)
Benedict spent $600 of his monthly salary and saved the rest. When he increased his spending by 35%, his savings decreased by 10%. How much, in $, was his monthly salary?
(NMOS 2015)
There are some marbles in a box. 40% of the marbles are red. There are 12 more yellow marbles than red marbles in the box and the rest of the marbles are green. If there is a total of 132 red and yellow marbles, what is the percentage of the green marbles in the box? (NMOS 2015)
The price of a shirt is reduced from Rp. 24.000,00 to Rp.18.000,00. If normally the profit is 60%, how many percent is the profit or loss after the price reduction? (OSN SD Uraian 2004)
Suatu kegiatan ekstrakurikuler yang diikuti oleh 100 anak menempati tiga ruangan A, B, dan C. Setelah satu bulan, 50% anak dari ruang A pindah ke ruang B, 20% anak dari ruang B pindah ke ruang C, dan sepertiga anak dari ruang C pindah ke ruang A. Setelah perpindahan terjadi, ternyata banyak anak di setiap ruangan tidak berubah. Berapakah banyak anak di ruang A? (OSN SD Uraian 2007)
Sebuah kotak berisi bola merah dan bola putih dengan 80% di antaranya adalah bola merah. Mula-mula diambil 35 bola merah dan 5 bola putih dari kotak tersebut. Sisanya dibagi menjadi beberapa kelompok, masing-masing terdiri atas 7 bola. Pada setiap kelompok terdapat 5 bola merah. Pada awalnya paling sedikit terdapat … bola dalam kotak tersebut. (OSN SD Isian Singkat 2010)
Seorang karyawan baru di sebuah perusahaan memulai kerja pada tanggal 1 januari dengan gaji per bulan sebesar 5 juta rupiah. Setelah bekerja 6 bulan gajinya naik sebesar 20%. Di akhir tahun dia harus menghitung pajak penghasilannya yang dihitung dari jumlah gajinya selama satu tahun. 18 juta rupiah dari gajinya setahun tidak kena pajak, dan sisanya kena pajak sebesar 5%. Berapa rata-rata pajaknya per bulan di tahun tersebut? (OSN SD Uraian 2015)
Harga satu buah baju di Toko A adalah Rp 5.000, 00 lebih mahal dibanding harga satu buah baju di toko B. Toko B memberikan diskon 10% untuk setiap baju sedangkan toko A memberi harga khusus jika seseorang membeli baju lebih dari satu buah, seseorang akan memperoleh diskon 40% untuk baju kedua yang dia beli. Dengan kondisi seperti itu ternyata harga dua buah baju di Toko A sama dengan harga dua buah baju di Toko B. Berapa harga satu buah baju di Toko A? (OSN SD Uraian 2011)
Perbandingan banyak siswa kelas A,B dan C adalah 2:3:4. Perbandingan nilai rata-rata ujian matematika kelas A,B dan C adalah 4:3:2. Rentang nilai ujian matematika 0 sampai dengan 100. Tentukan nilai rata-rata terbesar seluruh siswa yang mungkin. (OSN SD Uraian 2016)
Ali, Beni, dan Cepi masing-masing memilih satu bilangan positif. Mereka lalu membanding bandingkan yang mereka pilih sepasang-sepasang. Ada tiga rasio yang mereka dapatkan, ketiganya lebih kecil dari 1. Dua rasio adalah 2/5 and 5/7, sedangkan rasio ketiga adalah R, nilai R terbesar yang mungkin adalah … (OSN SD Isian Singkat 2008)
In a class, the ratio between the number of girls and boys is 4 : 5. If four boys go out, then the ratio becomes 1 : 1. How many girls are there in the class? (OSN SD Uraian 2009)
Alif memiliki 4 kotak kelereng yang masing-masing berisi 10, 15, 20 dan 28 butir kelereng. Alif mengambil sejumlah kelereng dari masing- masing kotak sehingga perbandingan banyak kelereng pada kotak tersebut menjadi 1:2:3:4. Banyaknya kelereng maksimal seluruhnya yang tersisa adalah ⋯ . (OSN SD Isian Singkat 2017)
Joko dan Badrun berdiri pada suatu antrian. Pada antrian tersebut, perbandingan antara banyaknya orang di depan dan di belakang Joko adalah 1:3. Sedangkan perbandingan antara banyaknya orang di depan dan di belakang Badrun adalah 2:5. Paling sedikit banyaknya orang pada antrian tersebut adalah (OSN SD Isian Singkat 2010)
Pada tahun 2009, perbandingan banyaknya rusa jantan dan rusa betina di suatu kebun binatang adalah 2:3. Pada tahun 2010 banyaknya rusa jantan bertambah 9 ekor dan banyaknya rusa betina berkurang 4 ekor, sehingga perbandingannya menjadi 3:2. Banyaknya rusa jantan pada tahun 2010 di kebun binatang tersebut adalah (OSN SD Isian Singkat 2010)
Pak Karto memiliki dua bidang tanah. Perbandingan luas tanah pertama dengan luas tanah kedua adalah 2 : 3. Ia menanam jagung dan kedelai pada tanah pertama maupun pada tanah kedua. Pada tanah pertama, perbandingan luas tanaman jagung dan luas tanaman kedelai adalah 1 : 3, sedangkan secara keseluruhan perbandingannya adalah 3 : 7. Berapakah perbandingan luas tanah yang ditanami tanaman jagung dan tanaman kedelai pada tanah ke- dua? (OSN SD Uraian 2010)
Alice and John had some sweets in the ratio 5∶7. After Alice gave John some sweets, the ratio of the number of sweets Alice had to that of John was 17∶31. Express the number of sweets that Alice gave John as a percentage of the number of sweets she had first. If your answer is m%, shade “m” as your answer. For example, if the answer 50%, shade “50”. (NMOS 2012)
Ali bought a camera from Betty, and then sold it to Cathy at a profit. If Ali had given Cathy a 10% discount, Ali would have made a $140 profit. If Ali had given Cathy a 5% discount, then Ali would have made a $200 profit. What was the price of the camera that Ali bought from Betty? (NMOS 2010)
The ratio of male students to female students in a primary school is 5:4. The ratio of students who wear spectacles to students who do not is 11:1. Given that 64% of the students who do not wear spectacles are female, find the percentage of female students who do not wear spectacles. (NMOS 2010 Special Round)
Kadar garam dalam enam liter air laut adalah 4%. Setelah air laut tersebut menguap sebanyak 1 liter, kadar garam menjadi ... persen. (OSN SD Isian Singkat 2007)
Wira mempunyai dua buah botol yaitu botol A dan botol B. Botol A berisi (3 )/4 air putih, dan botol B berisi (3 )/4 susu. Wira kemudian menuangkan isi botol A ke botol B sampai botol B terisi penuh, lalu botol B dikocok sehingga air dan susu tercampur rata. Setelah itu, campuran di botol B dituangkan ke dalam botol A sampai botol A terisi penuh. Perbandingan air dan susu yang ada dibotol A sekarang adalah . . . : . . . . (OSN SD Isian Singkat 2014)
Toko kopi Aroma mempunyai persediaan kopi arabika dan kopi robusta. Harga tiap kilo- gram kopi arabika adalah Rp.70.000, 00 sedangkan harga tiap kilogram kopi robusta adalah Rp.50.000, 00. Karena banyak konsumen yang menyukai kopi campuran antara arabika dan robusta, mereka mencampur kopi arabika senilai Rp.280.000, 00 dengan kopi robusta senilai Rp.300.000, 00. Berapa harga 1 kg kopi campuran tersebut? (OSN SD Uraian 2012)
A watermelon, with 92% of its weight being water, was left to stand in the sun. Some of the water evaporated so that now only 91% of its weight is water. The weight of the watermelon is now 4048 grams. What was the weight of the watermelon (in grams) before the water evaporated? (NMOS 2013)
A kind of drink contains 5% pure chocolate. If 5 liters of milk are added to 20 liters of this drink, find the percentage of chocolate in the mixture. (IMSO 2006 Essay Problem)
Fatimah wants to make a drink that contains 40% pure orange juice. This drink is called 40% orange juice. Her mom gives her 100ml of 20% orange juice, and a large bottle of drink that contains 80% pure orange juice. Fatimah needs . . . ml the drink in the bottle to produce the 40% orange juice. (IMSO 2008 Short Answer)
A big container is filled with 150 litres of syrup and 50 litres of water. Then 40 litres of the mixture is removed and the container is filled with water again to obtain the original volume. What is the percentage of the syrup in the final mixture? (NMOS 2008 Special Round)
A painter mixed different colours of paint in a pail. He mixed 8 litres of blue paint and 12 liters of yellow paint together in the pail to obtain green paint. Not satisfied with the colour of the mixture, he poured away 5 litres of the mixture and added blue paint to obtain the original volume. What percentage of the final mixture was made up to blue paint? (NMOS 2009)