# QUESTIONS ON RATIO & PROPORTION (PART-3)

## QUESTIONS ON RATIO & PROPORTION (PART-3)

#### QUERY 21

**An organization distributes its profit between its officers and clerks in the ration of 5 : 3. It has 45 officers and 80 clerks. Every officer earns Rs 5,000. Find its total profit earned.**

A) Rs 2,25,000

B) Rs 4,00,000

C) Rs 3,60,000

D) Rs 3,75,000

**MAHA GUPTA**

Profit to be distributed among officers = 5,000*45 = 2,25,000

So total of organization’s profit = 2,25,000 × ^{Ratio Sum}⁄_{Share of Officers}

= 2,25,000 × ^{8}⁄_{5} = 3,60,000 (option ‘C’)

QUERY 22

**The average of the work done by (x – 2) men in (x + 2) days and work done by (x + 3) men in (x – 2) days is 15 : 16. Find the value of ‘x’.**

A) 26

B) 13

C) 10

D) 12

**MAHA GUPTA**

Work done by (x – 2) men in (x + 2) days = (x – 2)(x + 2)

And work done by (x + 3) men in (x – 2) days = (x + 3)(x – 2)

Therefore ^{(x – 2)(x + 2)}⁄_{(x + 3)(x – 2)} = ^{15}⁄_{16}

=> ^{x+2}⁄_{x+3} = ^{15}⁄_{16}

=> x = 13 (option ‘B’)

QUERY 23

**4a = 5b, 7b = 9c, then f****ind a : b : c = ?**

A) 45 : 36 : 28

B) 30 : 36 : 25

C) 36 : 45 : 28

D) 36 : 30 : 25

**MAHA GUPTA**

4a = 5b

=> a/b = 5/4

=> a : b = 5 : 4 —-(i)

7b = 9c

=> b/c = 9/7

=> b : c = 9 : 7 —-(ii)

Multiplying (i) by 9 and (ii) by 4; means equalizing ‘b’

a : b : c = 45 : 36 : 28 (option ‘A’)

QUERY 24

**Two types of oil A and B are mixed in the ratio 3:2. 1/4th of the mixture is wasted. To the remaining mixture additional amount of oil A is mixed so that the ratio becomes 5:3. If the quantity of the new mixture be 1200 litre, find the quantity of original mixture and also additional amount of A mixed later.**

A) 1500, 50

B) 2000, 50

C) 2000, 75

D) 1500, 75

**MAHA GUPTA**

Oil ‘A’ in the new mixture = 1200*(5/8) = 750 liter

And oil ‘B’ in the new mixture = 1200*(3/8) = 450 liter

The change is made only in oil ‘A’, means oil ‘B’ is intact after the wastage. 1/4 of the original mixture was wasted, means oil ‘B’ too was wasted 1/4. Therefore we can say that 450 is (1 – 1/4) i.e. 3/4 of original quantity of oil ‘B’.

Hence oil ‘B’ in the original mixture = 450*(4/3) = 600 liter

But the original ratio was 3 : 2, therefore oil ‘A’ originally = 600*(3/2) = 900 litre

Wasted oil ‘A’ = 1/4 of 900 = 225 litre

Remaining original oil ‘A’ = 900 – 225 = 675 litre

Oil ‘A’ after addition = 750 litre

Hence addition of oil ‘A’ = 750 – 675 = 75 litre

And the quantity of the original mixture = 900 + 600 = 1500 litre

Thus option ‘D’ is correct.

SHORT

Take options one by one and match them with the given ratios, for example take option ‘D’

Original mixture = 1500

Mixture remained after wastage = 1500 – 1500/4 =1125

Now oil A in it = 1125 × 3/5 = 675

And oil B in it = 1125 × 2/5 = 450

Oil A after addition of 75 = 675+75 = 750

So the new ratio of A and B = 750 : 450 = 5 : 3 which is correct

QUERY 25

**If x : y = 3 : 4; then 4x + 5y : 5x – 2y is equal to?**

A) 7 : 32

B) 5 : 37

C) 14 : 3

D) 32 : 7

**MAHA GUPTA**

x : y = 3 : 4 => x/y = 3/4

Now, 4x + 5y = 4(x/y) + 5 —-(dividing both terms by y)

= 4(3/4) + 5 = 8

And, 5x – 2y = 5(x/y) + 2

= 5(3/4) – 2 = 7/4

Therefore, (4x + 5y) : (5x – 2y) = 8 : 7/4 = 32 : 7 (option ‘D’)

QUERY 26

**The ratio of A’s and B’s incomes last year was 3 : 4. The ratio of their own incomes of last year and this year is 4 : 5 and 2 : 3 respectively. If the sum of their present incomes is Rs 4160, find the present income of A.**

A) Rs 3000

B) Rs 3500

C) Rs 2600

D) Rs 1600

**MAHA GUPTA**

The ratio of A’s and B’s incomes last year was 3 : 4

Let A’s income last year = 3a

Therefore, B’s income last year = 4a

The ratio of A’s incomes last year and present year is 4 : 5

Let A’s income last year = 4x

Therefore A’s income present income = 5x

The ratio of B’s incomes last year and present year 2 : 3

Let B’s income last year = 2y

Therefore, B’s income present year = 3y

From above

3a = 4x ==> x = 3a/4

4a = 2y ==> y = 2a

Now, ratio of present incomes of A and B = 5x : 3y (from above)

Now putting values of x and y in the above equation

5*(3a/4) : 3*(2a)

==> 15 : 24

Hence A’s present income = 4160*(15/24) = 2600 (option ‘C’)