Question 1

Two numbers are in the ratio 3 : 5. If each number is increased by 10, the ratio becomes 5 : 7. The numbers are?

Accepted Answer

Let the number be 3a and 5a Then, (3a + 10) / (5a + 10) = 5/7 ∴ 7(3a + 10) = 5 x (5a + 10) ∴ 4a = 20 ∴ a = 5 So, the number are 15, 25.

Question 2

The ratio between Sumit's and Prakash's age at present is 2 : 3. Sumit is 6 years younger than Prakash. The ratio of Sumit's age to Prakash's age after 6 years will be?

Accepted Answer

Let their ages be 2x and 3x years. ∴ 3x - 2x = 6 ∴ x = 6 ∴ Sumit's age = 12 years, Prakash's age = 18 years After 6 years, Sumit's age = 18 years After 6 Years, prakash's age = 24 years ∴ Required ratio of their ages = 18 : 24 = 3 : 4

Question 3

The ages of Vivek and Sumit are in the ratio 2 : 3. After 12 years, their ages wiil be in the ratio 11:15. The age of Sumit is?

Accepted Answer

Let their ages be 2x and 3x years (2x + 12) / (3x + 12) = 11 /15 ⇒ 15(2x + 12) = 11(3x + 12) ⇒ 3x = 48 ∴ x = 16 ∴ age of sumit = 3x = 48 years

Question 4

The ratio of father's age to son's age is 4 : 1. The product of their age is 196. The ratio of their ages after 5 years will be?

Accepted Answer

Let their ages be 4x and x years. ∵ 4x2 = 196 ∴ x2 = 49 ⇒ x = 7 Their ages are 28 years and 7 years. Ratio of their ages be after 5 years = 33 : 12 = 11 : 4.

Question 5

The ratio between The ages of Kamla and Savitri is 6 : 5 and the sum of their age is 44 years.The ratio of their ages after 8 years wiil be?

Accepted Answer

Let their ages be 4x and x years. ∵ 6x + 5x = 44 ∴ x = 4 So their present ages are 24 years and 20 years Ratio of their ages after 8 years = 32 : 28 = 8 : 7.

Question 6

A father's age was 5 times his son's age 5 years ago, and will be 3 times son's age after 2 years the ratio of their present ages is?

Accepted Answer

Let son's age 5 years ago = x years. Then father's age at that time = 5x years. After 2 years, son's age = (x + 7) years. After 2 years, father's age = (5x + 5) ∵ 3(x + 7) = 5x + 7 ∴ x = 7 Father's age now = ( 5x + 5 ) = 40 years son's age now = (x+5) = 12 years ∴ Ratio of their present ages = 40 : 12 = 10 : 3

Question 7

The average age of 3 girls is 20 years and their ages are in the proportion 3 : 5 : 7. the age of youngest girl is?

Accepted Answer

Their total age = (3 x 20) yeras = 60 years Let their ages be 3x, 5x and 7x years. Then 3x + 5x + 7x = 60 ⇒ x = 4 ∴ yongest girl is = 3x = 12 years old.

Question 8

A man has some hens and cows. If the number of heads be 48 and number of feet equal 140 the number of hens will be?

Accepted Answer

Let the numbers of hens = x and number of cows = y Then x + y = 48 and 2x + 4y = 140 Solving these equations, we get 2y = 44 ∴ y = 22 So, x = (48 - 22) = 26 ∴ Number of hens = 26.

Question 9

6 man, 8 woman, 6 children complete a job for a sum of Rs. 950. if their individuals wages are in ratio 4 : 3 : 2, the total money earned by the children is?

Accepted Answer

Ratio of wages of 6 men, 8 women and 6 = (6 x 4) : (8 x 3) : (6 x 2) = 24: 24 : 12 = 2 : 2 : 1 ∴ Total money earned by children = Rs. (950 x 1/5) = Rs. 190

Question 10

The ratio between two numbers is 3 : 4 and their L.C.M. is 180. The first number is?

Accepted Answer

Let the numbers be 3x and 4x Then, their L.C.M. = 12x ⇒ 12x = 180 ∴ x = 15 Hence, the first number = 45

Question 11

In a mixture of 60 litres, the ratio of milk and water is 2 : 1. What amount of water must be added to make the ratio 1 : 2?

Accepted Answer

Milk = 60 x (2/3) litres =40 litres Water = (60 - 40) litres = 20 litres ∵ 40 / (20 + x) = 1/2 ⇒ 20 + x = 80 ∴ x = 60 Hence water to be added = 60 litres.

Question 12

A sum of Rs. 1300 is divided between A, B and C and D such that ( A's share / B's share ) = ( B's share / C's share ) = ( C's share / D's share ) = 2 / 3, Then A's share is?

Accepted Answer

∵ A : B = 2 : 3, B : C = 2 : 3 and C:D = 2 : 3 ⇒ A : B = 8 : 12, B : C = 12 : 18 and C : D = 18 : 27 ∴ A : B : C : D =8 : 12 : 18 : 27 So A's share = Rs. 1300 x ( 8 / 65) = Rs. 160

Question 13

Two equals glasses are respectively 1/3 and 1/4 full of milk. They are then filled up with water and the contents mixed in a tumbler, The ratio of milk and water in the tumbler is?

Accepted Answer

First glass contains milk = 1/3 and water = 2/3 Second glass contains milk = 1/4 and water = 3/4 ∴ Now tumbler contains water = (3/2 + 3/4) = 17/12 ∴ Ratio of milk and water =7/12 : 17/12 =7 : 17

Question 14

If a : b = c : d then, (ma + nc) / (mb + nd) is equal to?

Accepted Answer

Let (a/b) = (c/d) = k Then, a = bk and c = dk. ∴ (ma + nc) / (mb + nd) = (mbk + ndk) / (mb + nd) = k(mb + nd/mb + nd) = k = a/b = a : b.

Question 15

A mixture contains milks and water in the ratio 5 : 1. On adding 5 litres of water the ratio of milk and water becomes 5 : 2. The quantity of milk in the mixture is?

Accepted Answer

Let quantity of milk and water be 5x and x litres. Then, 5x / (x + 5) = 5/2 ∴ 10x = 5x + 25 ∴ x =5 ∴ Quantity of milk = 5x =25 litres

Question 16

A's money is to B's money as 4 : 5 and B's money is to c's money as 2 : 3. If A has Rs. 800, C has?

Accepted Answer

A : B = 4 : 5 = 8 : 10 and B : C = 2 : 3 = 10 : 15 ∴ A : B : C = 8 : 10 :15 If A has Rs. 8, C has Rs. 15 If A has Rs. 800 C has Rs. (15/8 x 100) = Rs. 1500

Question 17

15 litres of a mixture contains 20% alcohol and the rest water. If 3 litres of water be mixed in it. The percentage of alcohol in the new mixture will be?

Accepted Answer

Alcohol = (20/100) x 15 litres = 3 litres, Water = 12 litres New mix, contains, Alcohol = 3 litres, Water = 15 litres ∴ Percentage of alcohol in new mix. = (3/18) x 100 % = 162/ 3%

Question 18

Vinay got thrice as many marks in Maths as in English. The proportion of this marks in Maths and History is 4 : 3. If his total marks in Maths, English And History are 250. What are his marks in English?

Accepted Answer

M = 3E and M/H = 4/3 ∴ H = 3/4 M = 3/4 x 3E = 9/4 E Now M + E + H = 250 ⇒ 3E + E + 9/4 E = 250 ⇒ 25 E = 1000 ∴ E = 40

Question 19

Gold is 19 times as heavy as water and copper 9 times as heavy as water. The ratio in which these two metals be mixed so that the mixture is 15 times as heavy as water is?

Accepted Answer

Let, 1 gm of gold be mixed with y gm of copper to give (1 +x) gm of mixture. Now, 1G =19W and 1C = 9W and mixture = 15W Now, 1 gm gold + y gm copper = (1 + y) gm mixture ∵ 19 W + 9W x y = (1 + y ) x 15W Thus 4W = 6W x y ∴ y = 4W/6W = 4/6 = 2/3 So the required ratio is 1 : 2/3 i.e. 3 : 2

Question 20

Divide Rs. 600 among A, B and C so that Rs. 40 more than 2/5th of A's share,Rs. 20 more than 2/7th of B's share and Rs. 10 more than 9/17th of C's share may all be equal. What is A's share?

Accepted Answer

∵ 2A/5 + 40 = 2B/7 + 20 = 9C/17 + 10 = k ∴ A = 5(k - 40)/2, B =7(k - 20)/2 and C = 17(k - 10)/9 ⇒ 5(k - 40)/2 +7(k - 20)/2 +17/(k - 10 )/9 = 600 ⇒ 45k - 1800 + 63k - 1260 + 34k - 340 = 10800 ⇒ 142k = 14200 ∴ k = 14200 / 142 = 100 Hence A's share = (5/2) x ( 100 - 40) = Rs. 150

Ratio and Proportion Questions