RATIO AND PROPORTION
1. In a school, 10% of the boys are same in number as 1/5th of the girls. What is the ratio of boys to girls in that school?
(a) 1:2 (b) 3:4 (c) 3:2 (d) 2:1 (e) NOT
2. A sum of money is distributed among A, B and C such that A get double of C and B get average of A and B. find the ratio in which the money is distributed?
(a) 1:1:7 (b) 2:2:1 (c) 1:1:2 (d) 1:2:3 (e) NOT
3. Divide 27 into two parts so that 5 time the first and 11 times the second together equal to 195. Then ratio of the first and second part is:
(a) 10:17 (b) 17:10 (c) 10:13 (d) 1:2 (e) 5:7
4. The speed of a boat in still water is 500% more than the speed of the current. What is the respective ratio between the speed of boat downstream and speed of boat upstream?
(a) 4:9 (b) 5:7 (c) 5:6 (d) 11:2 (e) 7:5
5. In a class of 75 students, one-fifth of the total number of girls and three- fifth of total number of boys join a cricket club. If the total number of boys joining the club is 27. What is the respective ratio of the total number of boys to the total number of girls joining the club?
(a) 9:4 (b) 9:2 (c) 2:27 (d) 5:2 (e) NOT
6. In a class of 125, 20% students can dance. 2/5 of the total students can sing and 2/5 of the remaining students are good at sports. What is the respective ratio of students who can dance to students who are good at sport?
(a) 3:4 (b) 9:8 (c) 5:2 (d) 1:8 (e) 5:4
7. The respective ratio of the number of boys to girls studying in school is 25:29. The total number of students studying in the school is 270. If 15 boys and 15 girls take admission in the school. What will be the new respective ratio of the boys and girls studying in the school?
(a) 2:1 (b) 7:8 (c) 5:8 (d) 2:7 (e) 12:7
8. Two numbers are in the ratio of 3:5.if 9 is subtracted from each then they become 12:23. Find the numbers?
(a) 23,46 (b) 33,55 (c) 32,16 (d) 13, 28 (e) 14,28
9. The income of A, B and C are in the ratio of 7:9:12 and their spending are in the ratio 8:9:15. If A saves 1/4th of his income, then the saving of A, B and C are in the ratio of :
(a) 1:2:3 (b) 3:4:7 (c) 7:9:2 (d)data inadequate (e)NOT
10. The ratio of the number of boys and girls in a college is 5:6. If the percentage increase in the number of boys and girls are 25% and 30 % respectively, then find the new ratio?
(a) 120:131 (b) 125:156 (c) 123:121 (d) cannot be determined (e) NOT
11. In a bag, there are coins of 25p, 10p and 5p in the ratio of 1:2:3. If there is Rs. 30 in all, how many 5p coins are there?
(a) 750 (b) 100 (c) 150 (d) 200 (e) 450
12. Seats for mathematics, physics and English in a school are in the ratio 6:7:9. There is proposal to increase these seats by 40%, 30% and 60% respectively. What will be the ratio of increased seats?
(a) 13:45:34 (b) 13:34:45 (c) 84:91:144 (d) 15:26:31 (e) NOT
13. An amount of Rs. 2430 is divided among P, Q and R such that if their shares be reduced by Rs. 5, Rs. 10 and Rs. 15 respectively the remainders will be in the ratio of 3:4:5. Then Q‘s share was:
(a) 200 (b) 800 (c) 450 (d) 1200 (e) 1000
14. The ratio of the incomes of A and B is 5:4 and the ratio of their expenditure is 3:2. If at the end of the year, each saves 1600, then the income of B is :
(a) 1600 (b) 2400 (c) 3200 (d) 2000 (e) NOT
15. The side of triangles are in the ratio ½:1/3:1/4 and its perimeter is 104 cm. the length of the longest side
is:
(a) 32 cm (b) 20 cm (c) 54 cm (d) 56 cm (e) 48 cm
16. The ratio of third proportional to 16 and 26 and the mean proportional between 9 and 25 is :
(a)13:60 (b) 169:60 (c) 60:169 (d) 60:31 (e) 60:13
17. What is the ratio whose terms differ by 50 and the measure of which is 3/7?
(a) 2:5 (b) 4:5 (c) 3:7 (d) 5:7 (e) 5:8
18. It is given that x varies inversely as square of y, then z varies as cube of y. if y=3, then the ratio of x/z is?
(a) 1/9² (b) 1/9³ (c) 1/27³ (d) 1/3² (e)NOT
19. 40 kg of an alloy M is mixed with 100 kg of alloy N. if alloy M has silver and gold in ratio 3:2 and alloy N has silver and gold in ratio 1:4, then the ratio of silver and gold in the new alloy is :
(a) 11:24 (b) 23:14 (c) 4:25 (d) data inadequate (e) NOT
20. The ratio between product of two numbers and difference of two numbers if 45:2, what is the ratio of LCM/ HCF of two numbers?
(a) 1:2 (b) 3:4 (c) 3:4 (d) data inadequate (e) NOT
21. Ravi invest in two schemes in the ratio 12:17 for two years, after that he increase his investment by 15%, what is the ratio of the profit he got in two schemes?
(a) 4:19 (b) 5:14 (c) data inadequate (d) 14:11 (e) NOT
22. The ratio of two consecutive odd numbers is in ratio 14:27. What is the ratio of difference and sum of these two numbers?
(a) 54:13 (b) 26:81 (c) 13:28 (d) 13:41 (e) 12:25
23. In a school 20 % of literate boys are same as illiterate girls and literate girls are 1/5 of illiterate boys. What is the ratio between total boys and total girls?
(a) 4:1 (b) 5:1 (c) 6:1 (d) cannot be determined (e) NOT
24. The average age of three girls is 25. Fifteen year hence, the ratio is in the proportion 3:5:7. The age of youngest girl is?
(a) 20 (b) 24 (c) 25 (d) 23 (e) NOT
25. If 10% of x is 45% of y and 35% of y is 12% of z then x: y: z is?
(a) 12:10:35 (b) 9:2:45 (c) 6:10:15 (d) 54:12:35 (e)NOT
26. Three containers have their volumes in the ratio 3:4:5. They are full of mixture s of milk and water. The mixtures contain milk and water in the ratio of (4:1), (3:1) and (5:2) respectively. The contents of all these three containers are poured into a fourth container. The ratio of milk and water in the fourth container is :
(a) 157:53 (b) 1:1 (c) 3:20 (d)34:19 (e) NOT
27. Rajiv has 14 currency notes in his pocket consisting of only Rs. 20 and Rs. 10 notes. The total money value of the notes is Rs. 230. The ratio of Rs. 10 notes to Rs. 20 that Rajiv has is:
(a) 4/5 (b) 1/6 (c) 1/1 (d) 5/9 (e) NOT
28. A, B and C share a sum of money in the ratio 7:8:16. If C receives Rs. 27 more than A, then the total money shared was?
(a) 65 (b) 93 (c) 445 (d) 450 (e) 280
29. A, B and C can complete a work in 2, 3 and 4 days respectively. If they complete the work together, in what ratio they should divide the money?
(a) 3:2:4 (b) 4:5:9 (c) 5:6:7 (d) 2:9:1 (e) 6:4:3
30. Two cogged wheels of which one has 16 cogs and other 27, work into each other. If the latter turns 80 times in three quarters of a minute, how often does the other turn in 8 second?
(a) 12 (b) 26 (c) 24 (d) 48 (e) 96
31. If ½ of the number of white mice in a certain laboratory is 1/8 of the total number of mice and 1/3 of the number of grey mice is 1/9 of the total number of mice, then what is the ratio of white mice to grey mice?
(a) 2:3 (b) 4:5 (c) 3:4 (d) 3:7 (e) 16:27
32. The ratio of incomes of John and Joe is 3:5 and ratio of their expenditure is 5:1. Who saves more?
(a) John (b) Joe (c) neither of them (d) cannot be determined (e) NOT
33. A and B can complete a work in 2 & 3 days respectively. They complete a work together and get Rs. 50 as the wages. How should they divide it?
(a) 1:2 (b) 1:3 (c) 1:5 (d) 3:2 (e) 3:1
34. A certain ship floats with 3/5 of its weight above the water. What is the ratio of the ship‘s submerged weight to its exposed weight?
(a) 3:8 (b) 3:5 (c) 2:3 (d) 2:5 (e) NOT
35. If a carton containing dozen mirrors is dropped, which of the following cannot be the ratio of broken to unbroken mirrors?
(a) 1:1 (b) 2:1 (c) 3:2 (d) 3:1 (e) NOT
SOLUTION AND EXPLANATION OF RATIO AND PROPORTION
1. (d)
10% of boys = 1/5 of girls
Boys/girls = 1/5: 1/10/100 = 2:1
2.(b)
According to the question,
A= 2C and B =A+B/2,
A: B: C = A: A: A/2 = 1:1:1/2 = 2:2:1.
3.(b)
Let the first number be 27-x and second number be x,
5(27-x) +11x = 195,
Then x = 10, so the ratio is 17/10.
4.(e)
Let speed of boat in still water is u and speed of current is v
Then u =6v
Ratio= speed of downstream: speed of upstream = u+v: u-v = 7:5
5.(b)
Given, 3/5 of total boys joined the club = 27, so total boys = 45,
Total girls = 75-45 = 30,
Girls joining club = 1/5 * 30 = 6.
Ratio is = 27/6 = 9/2.
6.(e)
Ratio is = 5/4.
7.(b)
Boys/girls = 25/29, boys + girls = 270,
Then girls = 145 and boys = 125,
After admission of 15 boys and 5 girls new ratio = 140/160 = 7/8.
8.(b)
Let the numbers be x and y,
Then numbers are 33, 55.
9.(e)
Income of A, B & C are in ratio of 7:9:12 and their spending in the ratio of 8:9:15.
For A, 7x- 8y =7/4x, then x= 32y/21, savings of A, B & C is 7/4x: 9(x-y): 12x-15y
On putting the value of x = 32y/21 in the ratio we get ratio as 56:99:69.
10.(b)
The new ratio between boys and girls are
11.(c)
Let the total number of coins be x. then,
60x/100 = Rs. 30
Then x= 50,
5p coins = 3*50 = 150.
12.(c)
The new ratio is = 6 * 140/100: 7* 130/100: 9 * 160/100= 84:91:144.
13.(b)
Total reduced amount = 2430 – (5+10+15) = 2400.
Q‘s share =
14.(c)
Let the income be x and expenditure be y,
Then, 5x-3y = 1600
And 4x- 2y = 1600
On solving both equation, we get x = 800, income of B = 4x = 3200.
15.(e)
Let the side of triangle be a, b, and c so a+b+c = 104cm,
Also a: b: c = ½:1/3:1/4.
x/2 +x/3 + x/4 = 104 cm
x = 96
Longest side is x/2 = 48 cm.
16.(b)
Third proportion of 16:26 is 169/4 and mean of 9 and 25 is (9*25)^1/2 = 3*5 = 15
Ratio is 169/4:15 = 169:60.
17.(c)
Let the number be x and x+50, then x: x+50 = 3:7.
Then x = 75/2.
Ratio is 75/2: 175/2 = 3/7.
18.(e)
As per the question, x = 1/y² and z = y³, so ratio of x/z = 1/y^5 = 1/243
19.(a)
In alloy M, silver is 3/5 * 40 = 24 kg.
In alloy N silver is 1/5*100 = 20 kg,
Total silver content in new mixture is 44 kg,
Ratio of silver to gold in new mixture is 44/96 = 11/24.
20.(d)
Let the numbers be x and y, x*y/x-y = 45/2.
Since no other data is given
We cannot calculate HCF and LCM so data inadequate.
21.(c)
Initial investment = 12:17, after increase investment = 12:17,
We cannot calculate the profit ratio as no other information is given regarding profit received by him.
22.(a)
Given, a/a+2 = 14/27, then two consecutive odd number = 28/13, 54/13
Ratio = 26/13: 82/13 = 13:41.
23.(b)
20% of literate boys = illiterate girls
And literate girls = 1/5 * illiterate boys
Ratio of total boys and total girls = 5:1
24.(b)
Let the three girls be a, b and c,
Then a+b+c = 25*3
After 15 years a+b+c = 120
And their ratio of age after 15 year is given as 3:5:7,
So on using above data we get age of youngest girl = 24.
25.(d)
According to the question,
10/100x = 45/100y so x/y = 9/2
Also 35/100y = 12/100z,
And y/z =12/35
So x: y: z = 54:12:35
26.(a)
Let the three containers contain 3x, 4x and 5x litres of mixtures respectively
Milk and water in 1st mixtures is 12x/5 and 3x/5 litres.
Similarly milk and water in 2nd mixture is 3x and x.
And milk and water in 3rd mixture is 25x/7 and 10x/7 litres.
Total milk in final mixture = 314x/35 litres.
Total water in final mixture = 106x/35 litres.
Ratio of water milk to water = 157:53.
27.(d)
Let the 20 rupees note be x and 10 rupees note be y.
From the question it is known that x+y = 14
And 2x + y =23.
X =9 and y= 5.
Ratio is 5/9.
28.(b)
Ratio of A, B & C is 7:8:16.
Difference of A and C is 9x.
As per the question 9x = 27, x = 3.
Total money = 31 * 3 = 93.
29.(e)
Efficiency of A: Efficiency of B: Efficiency of C = ½:1/3:1/4 = (6:4:3)/12
So ratio is 6:4:3.
30.(c)
By using chain rule
27*8*80 = x*45*16.
Then x= 24 times.
31.(c)
½ of white mice = 1/8 of total mice
And 1/3 of grey mice = 1/9 of total mice.
White mice/grey mice = ¼: 1/3 = 3:4
32.(d)
Saving = income-expenditure
More data is needed to answer the question.
33. (d)
Rs. 50 is to be divided in the ratio of their efficiency,
Efficiency of A: efficiency of B = ½:1/3 = 3:2/6 = 3:2.
34.(c)
Ship submerged weight: exposed weight = 2/5: 3/5 = 2:3.
35.(c)
From all the options, option (c) cannot be the ratio as 2+3 = 5 is not a factor of 12.
