Exercise : 3


1. The ratio of number of students studying Arts, Commerce and Science in a College is 3 : 5 :8. What is the new ratio of the number of students studying Arts, Commerce and Science respectively if there is an increase of 20%, 40% and 25% in the number of students studying Arts, Commerce and Science?
(a) 18 : 35 : 50
(b) 3 : 10 : 10
(c) 4 : 8 : 5
(d) 32 : 35 : 25
(e) None of these
Ans.a

Suppose the number of students studying Arts, Commerce and Science be 3x, 5x and 8x respectively.

When their numbers are increased by 20%, 40% and 25% respectively the new ratio becomes

3x × 120% : 5x × 140% :

8x × 125% = 36 : 70 : 100

= 18 : 35 : 50

2. Abhishek started a business investing 50,000. After one year he invested another 30,000 and Sudin also joined him with a capital of 70,000. If the profit earned in three years from the starting of business was 87,500, then find the share of Sudin in the profit
(a) 37,500
(b) 32,500
(c) 38,281
(d) 52,500
(e) None of these
Ans.e

Ratio of Abhishek and Sudin for one month

= (50,000 × 36) + (30,000 × 24) : (70,000 × 24)

= (18,00,000 + 7,20,000) : 16,80,000 = 3 : 2

Hence share of Sudin in the profit earned from the business.

= \(\frac{87,500}{\left(3 + 2 \right)}\times 2\) = 35,000

3. Weights of two friends Ram and Shyam are in the ratio of 4 : 5. Ram’s weight increases by 10% and the total weight of Ram and Shyam together becomes 82.8 kg, with an increase of 15%. By what per cent did the weight of Shyam increase?

(a) 12.5%
(b) 17.5%
(c) 19%
(d) 21%
(e) None of these
Ans.c

Let the weights of Ram and Shyam be 4x and 5x. Now,according to question,

\(\frac{4x \times 110}{100} + Shyam?s \; new \; wt\) = 82.8........ (i)

and 4x + 5x = \(\frac{9x + 115}{100}\) = 82.8........ (ii)

From (ii), x = 8

Putting in (i),

we get Shyam’s new wt = (82.8 – 35.2) = 47.6

% increase in Shyam’s wt = \(\left(\frac{47.6 - 40}{40} \times 100 \right)\) = 19%

4. When 50% of one number is added to a second number,the second number increases to its four-thirds. What is the ratio between the first number and the second number?
(a) 3 : 2
(b) 3 : 4
(c) 2 : 3
(d) Data inadequate
(e) None of these
Ans.c

Let the numbers be y and x respectively

x + 50% of y = 4x3 or, y2 = 4x3 - x

or, y2 = x3

or, yx = 23

5. The ratio of present ages of Nisha and Shilpa is 7 : 8 respectively. Four years hence this ratio becomes 9 : 10 respectively. What is Nisha’s present age in years?
(a) 18
(b) 14
(c) 17
(d) Data inadequate
(e) None of these
Ans.b

Nisha            Shilpa
7                      8
4     9                     10

Present age of Nisha = \(\frac{4 \times \left(10 - 9\right)}{9 \times 8 - 10 \times 7} \times 7\)

= 14 years

6. When a number is added to another number the total becomes 3313 per cent of the second number. What is the ratio between the first and the second number?
(a) 3 : 7
(b) 7 : 4
(c) 7 : 3
(d) Data inadequate
(e) None of these
Ans.c

Let the first and second numbers be x and y respectively.

Then, x + y = 103y

or, x = 73y

∴ x : y = 7 : 3

7. The ratio between the present ages of P and Q is 5 : 8. After four years, the ratio between their ages will be 2 : 3. What is Q’s age at present?
(a) 36 years
(b) 20 years
(c) 24 years
(d) Data inadequate
(e) None of these
Ans.e

PQ = 58 or P = 5Q8 .....(i)

\(\frac{P + 4}{Q + 4} = \frac{2}{3}\)

or, 3P + 12 = 2Q + 8 or, 2Q – 3P = 4... (ii)

Putting value of P from eq. (i),

2Q – 3 × 58Q = 4 ⇒ Q = 32

8. Jaydeep purchased 25 kg of rice at the rate of 16.50 per kg and 35 kg of rice at the rate of 24.50 per kg. He mixed the two and sold the mixture. Approximately, at what price per kg did he sell the mixture to make 25 per cent profit?
(a) 26.50
(b) 27.50
(c) 28.50
(d) 30.00
(e) 29.00
Ans.a

CP = 25 × 16.50 + 35 × 24.50 = 1270

SP = 1270 × 125100 = 1587.50

Price per kg = 1587.5060 ≈ 26.50

9. In 1 kg mixture of sand and iron, 20% is iron. How much sand should be added so that the proportion of iron becomes 10%?
(a) 1 kg
(b) 200 gms
(c) 800 gms
(d) 1.8 kg
(e) None of these
Ans.a

In 1 kg mixture quantity of iron = 200 gm

Let x gm sand should be added, then

10% of (1000 + x) = 200

\ x = 1000 gm = 1 kg

10. The ratio of P's and Q's ages is 5 : 7. If the difference between the present age of Q and the age of P six years hence is 2 then what is the total of present ages of P and Q?
(a) 52 years
(b) 48 years
(c) 56 years
(d) Data inadequate
(e) None of these
Ans.d

PQ = 57

or, Q = 75P

Case I : Q – (P + 6) = 2

or, Q = P + 8

75P = P + 8

or, 7P = 5P + 40

∴ P = 402 = 20 and Q = 75 × 20 = 28

P + Q = 20 + 28 = 48

Case II : (P + 6) – Q = 2

or, P + 6 – 75P = 2

or, P = –10 and Q = 14

∴ P + Q = 10 + 14 = 24 years