Question

The incomes of X and Y are in the ratio of 8:7 and their expenditures are in the ratio 19:16. If each saves ? 1250, find their incomes.​

Answer 1

Given:

income of X : Y = 8 : 7

expenditure of X : Y = 19 : 16

Each save $1250

To Find:

Their income

Solution

Define E and M:

Let E be the expenditure factor

Let M be the income factor

expenditure of X : Y = 19 : 16

X = 19E

Y = 16E

income of X : Y = 8 : 7

X = 8M

Y = 7M

Form the equations:

19E + 1250 = 8M  --------- [ 1 ]

16E + 1250 = 7M  --------- [ 2 ]

Eqn [ 1 ] x 7 :

133E + 8750 = 56M --------- [ 1A ]

Eqn [ 2 ] x 8 :

128E + 10000 = 56M --------- [ 2A ]

[ 1A ] - [ 2A ] :

5E - 1250 = 0

5E = 1250

E = 250

Sub E = 250 into [ 1 ]:

19(250) + 1250 = 8M  

2250 + 1250 = 8M

8M = 3500

M = 437.5

Find their income:

X = 8M

X = 8(437.5)

X = $3500

Y = 7M

Y = 7(437.5)

Y = $3062.50

Answer: X's income = $3500 and Y's income = $3062.50

Answer 2

Let the income be denoted by x and the expenditure be denoted by y. 

Then, from the question we have

The income of X is ₹ 8x and the expenditure of X is 19y.

The income of Y is ₹ 7x and the expenditure of Y is 16y. 

So, on calculating the savings, we get 

Saving of X = 8x – 19y = 1250 

Saving of Y = 7x – 16y = 1250 

Hence, the system of equations formed are

8x – 19y – 1250 = 0

7x – 16y – 1250 = 0

Step-by-step explanation:

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