Question

A and b earn in the ratio of 2:3. they spend money in the ratio of 1:2 and save in the ratio of 4:1. if the total monthly savings of both is rs 1000,the monthly income of a is?

Answer 1

Find the amount each saved:

Saving of A : B = 4 : 1

Let k be the constant ratio.

4k + 1k = 1000

5k = 1000

k = 200

4k = 200 x 4 = 800

Saving of A : B = 800 : 200

.

Earning of A : B = 2 : 3

Let x be the constant ratio

Earning of A : B = 2x : 3x

.

Spending of A : B = 1 : 2

let y be the constant ratio

Spending of A : B = y : 2y

.

Form equations and solve for x and y:

2x - y = 800 ----------- [1]

3x - 2y = 200 ---------[2]

{1} x 2: 4x - 2y = 1600---------[3]

[3 - [2] : x = 1400

Sub x = 1400 into [1]:

2(1400) - y = 800

2800 - y = 800

y = 2000.

.

Find their income:

A = 2x = 2(1400) = 2800

B = 3x = 3(1400) = 4200

.

Answer: A earns Rs 2800 and B earns Rs 4800.