Question

The ratio of income of a, b and c is 2 : 3 : 4 and the ratio of expenditure is 3 : 4 : 5 . Savings of a is 1 5 of its income then find the ratio of their savings.

Answer 1

Given :   The ratio of income of a, b and c is 2 : 3 : 4  

ratio of expenditure is 3 : 4 : 5

Savings of a is 1/5 of its income  

To Find :   ratio of their savings.

Solution:

The ratio of income of a, b and c is 2 : 3 : 4  

Let say income of a  = 30k

then income of b = 45k

and income of c =  60k

Savings of a is 1/5 of its income   => Saving = (30k/5) = 6k

expenditure of A   =30k - 6k  = 24k

ratio of expenditure is 3 : 4 : 5  

=> b expenditure = (24k/3)*4  = 32k

 c expenditure = (24k/3)*5  = 42k

Saving of b = 45k - 32k  =  12k

saving of c = 60k - 42k = 18k

6k : 12k : 18k

= 1 : 2: 3

ratio of their savings. = 1 : 2: 3

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Answer 2

$\huge\sf {Solution:-}$

Let’s A’s income, B’s income, C’s income be Rs 7x, Rs 9x, and Rs 12x respectively and their expenditures be Rs 8y, Rs 9y and Rs 15y respectively.

Income= Expenditure + Saving

Saving= Income - Expenditure

7x-8y=7x/4

=> 4(7x-8y)=7x

=> 28x-32y=7x

=>28x-7x=32y

=> 21x=32y

=> y=21x/32

A’s Saving = 7x/4

B’s Saving = 9x-9y

=> 9(x-y)

put y= 21x/32

=> 9(x-21x/32)

=> 9(32x-21x/32)

=> 9(11x/32)

=> 99x/32

C’s Saving= 12x-15y

put y=21x/32

=> 12x - 15(21x/32)

=> 12x -315x/32

=> 384x-315x/32

=> 69x/32

Hence the required ratio,

7x/4, 99x/32, 69x/32

56:99:69