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Exercise : 2

1. Salaries of Rajesh and Sunil are in the ratio of 2 : 3. If the salary of each one is increased by 4000 the new ratio becomes 40 : 57. What is Sunil’s present salary?

(a) 17000

(b) 20000

(c) 25500

(d) Cannot be determined

(e) None of these

**Ans.e**
Let the salaries of Rajesh and Sunil be 2x and 3x respectively.

Then, \(\frac{2x + 4000}{3x + 4000} = \frac{40}{57}\)

or, 114x + 228000 = 120x + 160000

or, 6x = 68000

or, 3x = 34000

2. The numbers of students speaking English and Hindi are in the ratio of 4 : 5. If the number of students speaking English increased by 35% and that speaking Hindi increased by 20%, what would be the new respective ratio?

(a) 19 : 20

(b) 7 : 8

(c) 8 : 9

(d) Cannot be determined

(e) None of these

**Ans.e**
Reqd ratio = \(\frac{4 \times 135}{5 \times 120} = 9 : 10\)

3. Abhijit started a business investing 70000. Anuja joined him after six months with an amount of 105000 and Sunil joined them with 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Abhijit, Anuja and Sunil respectively, three years after Abhijit started the business?

(a) 42 : 45 : 56

(b) 7 : 6 : 10

(c) 12 : 15 : 16

(d) Cannot be determined

(e) None of these

**Ans.c**
Ratio of their investments

= 70 × 36 : 105 × 30 : 140 × 24 = 12 : 15 : 16

4. The ratio of males and females in a city is 7 : 8 and the percentage of children among males and females is 25% and 20% respectively. If the number of adult females in the city is 156800 what is the total population?

(a) 245000

(b) 367500

(c) 196000

(d) 171500

(e) None of these

**Ans.b**
Number of females = 156800 × ^{100}⁄_{80} = 196000

\ Number of males = ^{7}⁄_{8} × 196000 = 171500

\ Total population = 196000 + 171500 = 367500

5. Hariprasad and Madhusudan started a business, investing sums in the ratio of 2 : 3. If Hariprasad had invested an additional amount of 10,000 the ratio of Hariprasad's investment to Madhusudan's investment would have been 3 : 2. What was the amount invested by Hariprasad?

(a) 8000

(b) 12000

(c) 9000

(c) Data inadequate

(e) None of these

**Ans.a**
Let the initial investments of Hariprasad and Madhusudan be 2x and 3x,respectively.

From the question,

\(\frac{2x + 10000}{3x} = \frac{3}{2}\)
or, 4x + 20000 = 9x

\ x = 4000

\ Amount invested by Hariprasad = 2x = 8000

6. The ratio of the present ages of a son and his father is 1 : 5 and that of his mother and father is 4 : 5. After 2 years the ratio of the age of the son to that of his mother becomes 3 : 10. What is the present age of the father?

(a) 30 years

(b) 28 years

(c) 37 years

(d) Data inadequate

(e) None of these

**Ans.e**
^{S}⁄_{F} = ^{1}⁄_{5} ⇒ F = 5S

^{M}⁄_{F} = ^{4}⁄_{5} ⇒ M = ^{4}⁄_{5} F

\(\frac{S + 2}{M + 2} = \frac{3}{10}\)
10S + 20 = 30 M + 6 = 3 × ^{4}⁄_{5} 5S + 6 = 12S + 6

\ 2 S = 14 ⇒ S = 7 years

\ F = 5S = 35 years

7. The ratio of the number of students appearing for examination in the year 1998 in the states A, Band C was 3 : 5 : 6. Next year if the number of students in these states increases by 20%, 10% and 20% respectively, the ratio in states A and C would be 1 : 2. What was the number of students who appeared for the examination in the state A in 1998?

(a) 7200

(b) 6000

(c) 7500

(d) Data inadequate

(e) None of these

**Ans.d**
Let the number of students appearing for examination in the year 1998 in the states A, B and C be 3x, 5x and 6x respectively.

According to the question,

\(\frac{3x \times \frac{120}{100}}{6x \times \frac{120}{100}} = \frac{1}{2}\)
Hence data inadequate.

8. A man spends 1810 for buying bed sheets at 200 each and pillows at 70 each. What will be the ratio of bed sheets to pillows when maximum number of bed sheets are bought?

(a) 3 : 8

(b) 8 : 3

(c) 9 : 1

(d) 1 : 9

(e) None of these

**Ans.b**
The man can’t purchase more than 8 bedsheets

∴ cost of 8 bedsheets = 8 × 200 = 1600

Remaining amount = 1810 – 1600 = 210

And in 210, the man can purchase

^{210}⁄_{70} = 3 pillows

Reqd ratio = 8 : 3

9. Mr Shivkumar started a business, investing 25000 in 1996. In 1997 he invested an additional amount of 10000 and Mr Rakesh joined him with an amount of 35000. In 1998, Mr Shivkumar invested another additional amount of 10000 and Mr Suresh joined them with an amount of 35000. What will be Rakesh’s share in the profit of 150000 earned at the end of three years from the start of the business in 1996?

(a) 70000

(b) 50000

(c) 45000

(d) 75000

(e) None of these

**Ans.b**
Ratio of their investments = 25,000 × 1 + 35000 × 1 + 45000 × 1 : 35000 × 2 : 35000 × 1 = 3 : 2 : 1.

∴ Rakesh’s share = ^{2}⁄_{6} × 150000 = 50000

10. Incomes of two companies A and B are in the ratio of 5 : 8. Had the income of company A been more by 25 lakh, the ratio of their incomes would have been 5 : 4. What is the income of company B?

(a) 80 lakh

(b) 50 lakh

(c) 40 lakh

(d) 60 lakh

(e) None of these

**Ans.c**
Let the incomes of two companies A and B be 5x and 8x respectively.

From the question,

\(\frac{5x + 25}{8x} = \frac{5}{4}\) ⇒ 20x + 100 = 40x

∴ x = 5

∴ Income of company B = 8x = 40 lakh