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 find 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’)