Question

The ratio of the monthly incomes of A and B is 3: 4. The ratio of the monthly expenditure of A
and Bis 4:5. Which of the following represents a possible value of the ratio of their savings?
(A)9:10
(B)3:4
(C)13:20
(D) 4:5​

Answer 1

Answer:The monthly income of A and B are in the ratio of 3 : 4

Let the rational between incomes of A and B be x. Thus the income of A is 3x and income of B is 4x

Their monthly expenditure are in the ratio of 4 : 5

Let the rational between expenditure of A and B be y. Thus, the expenditure of A is 4y and expenditure of B is 5y

We know Savings = Income - expenditure

The respective Savings of A and B are in the ratio of 13 / 20. Therefore savings of A and B are

3x - 4y and 4x - 5y

Their ratio

3x - 4y / 4x - 5y = 13 / 20

hence, the ratio is 13:20

Answer 2

Answer:

(C)13:20

Step-by-step explanation:

As per the question:

A’s & B’s , income ratio= 3:4 ie, their income is 3x & 4x

Expenditure ratio = 4:5, ie, their expenditure = 4y & 5y..

Now, since we need to calculate the ratio of their differences ie, (3x-4y) : (4x-5y)

For this it impiles that x>y to make the savings positive.

If we try to put all the ratio’s one by one

From ( 9:10) We get x:y = 5:6 ( so it contradicts the condition of saving is to be positive).

From (3:4) We get y=0( which is not possible because expenditure can’t be 0).

From ( 13:20) We get x:y = 15:8 ( so it satisfies the condition of saving is to be positive).

From (4:5) We get x=0( which is not possible because Income can’t be 0).

so from the above deduction 13:20 is the only ratio.