Exercise : 5


1. Mr. Gangadhar, Mr. Ramesh and Mr. Shridhar together earned 19800. The ratio of earnings between Mr. Gangadhar and Mr. Ramesh is 2 : 1 while that between Mr.Ramesh and Mr. Shridhar is 3 : 2. How much did Mr. Ramesh earn?
(a) 3600
(b) 5400
(c) 1800
(d) 6300
(e) None of these
Ans.b

Ratio of investment = 6 : 3 : 2

∴ Share of Mr. Ramesh = 311 × 19800 = 5400

2. Mr. Kutty has only hens and sheep. If the total number of their heads is 38 and the total number of legs is 100 then what is the ratio between the numbers of hens and sheep?
(a) 2 : 1
(b) 1 : 2
(c) 6 : 13
(d) 13 : 6
(e) None of these
Ans.d

Let the total number of hens and sheep be x and y respectively.

i.e., x + y = 38 and 2x + 4y = 100

∴ Ratio = 13 : 6

3. If A : B : C = 2 : 3 : 4, then AB : BC : CA is equal to :
(a) 4 : 9 : 16
(b) 8 : 9 : 12
(c) 8 : 9 : 16
(d) 8 : 9 : 24
Ans.d

Let A = 2x, B = 3x and C = 4x. Then,

AB = 2x3x = 23, BC = 3x4x = 34 and CA = 4x2x = 21

AB : BC : CA = 23 : 34 : 21 = 8 : 9 : 24

4. A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets 1000 more than D, what is B’s share?
(a) 500
(b) 1500
(c) 2000
(d) 1400
(e) None of these
Ans.c

Let the shares of A, B, C and D be 5x, 2x, 4x, 3x respectively.

Then, 4x – 3x = 1000 ⇒ x = 1000

∴ B’s Share = 2x = 2000

5. The sum of three numbers is 98. If the ratio of the first to the second is 2 : 3 and that of the second to the third is 5 : 8,then the second number is :
(a) 20
(b) 30
(c) 38
(d) 48
(e) None of these
Ans.b

A : B = 2 : 3 = 2 × 5 : 3 × 5 = 10 : 15

and B : C = 5 : 8 = 5 × 3 : 8 × 3 = 15 : 24

Therefore, A : B : C = 10 : 15 : 24

∴ A : B : C = 10 : 15 : 24

Let the number be 10x, 15x and 24x.

Then, 10x + 15x + 24x = 98

or 49x = 98 or x = 2

⇒ Second number = 15x = 15 × 2 = 30

6. The ratio of number of ladies to gents at a party was 1 : 2, but when 2 ladies and 2 gents left, the ratio became 1 : 3. How many people were originally present at the party?
(a) 6
(b) 9
(c) 12
(d) 10
(e) None of these
Ans.c

Let number of ladies = x

then, number of gents = 2x

Now, \(\frac{x - 2}{2x - 2} = \frac{1}{3}\) ⇒ 3x - 6 = 2x - 2

⇒ x = 4

∴ Total number of people originally present = 4 + 8 = 12

7. A man divides his property so that his son’s share to his wife’s and the wife’s share to his daughter are both in the ratio 3 : 1. If the daughter gets 10,000 less than the son, find the total worth of the property.
(a) 16,200
(b) 16,250
(c) 16,500
(d) 15,300
(e) None of these
Ans.b

Let Son’s share = S;

Daughter’s share = D;

and Wife’s share = W.

Also, S : W = W : D = 3 : 1

∴ S : W : D = 9 : 3 : 1

then S = 9x , D = x

and 9x – x = 10,000 ⇒ x = 1250

∴ Total worth of the property = (9 + 3 + 1)x = 13x

= 13 × 1250 = 16,250

8. A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is 35, how many coins of each type are there?
(a) 20 coins
(b) 30 coins
(c) 28 coins
(d) 25 coins
(e) None of these
Ans.a

Let number of each type of coin = x. Then,

1 × x + .50 × x + .25x = 35

⇒ 1.75x = 35 ⇒ x = 20 coins

9. The salaries of A,B,C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be the new ratio of their salaries?
(a) 3 : 3 : 10
(b) 10 : 11 : 20
(c) 23 : 33 : 60
(d) Cannot be determined
(e) None of these
Ans.c

Let A = 2k, B = 3k and C = 5k.

A’s new salary = 115100 of 2k = (115100 × 2k) = 2310k

B’s new salary = 110100 of 3k = (110100 × 3k) = 3310k

C’s new salary = 120100 of 5k = (120100 × 5k) = 6k

∴ New ratio = 23k10 : 33k10 : 6k = 23 : 33 : 60

10. In an express train, the passengers travelling in A.C. sleeper class, First class and Sleeper class are in the ratio 1 : 2 : 7, and rate for each class is in the ratio 5 : 4 : 2. If the total income from this train is 54,000 , find the income of Indian Railways from A.C. sleeper class.
(a) 12,000
(b) 20,000
(d) 22,000
(d) 10,000
(e) None of these
Ans.d

Let number of passengers = x, 2x, 7x

and Rate = 5y, 4y, 2y

Now, since income = Rate × Number of passengers

∴ Income = 5xy, 8xy, 14xy

∴ Income in ratio = 5 : 8 : 14

∴ Income from A.C. sleeper class = \(\frac{5}{5 + 8 + 14} \times 54,000\)

= 10,000