Question

The incomes of two persons A and B are in the ratio 8:7 and the ratio of their expenditure is 19:16.If their savings are rupees 2550 per month, find their monthly income.

Answer 1

Answer: A's income  is Rs.12240

B's income is Rs. 10710

Step-by-step explanation:

The incomes of two persons A and B are in the ratio 8:7

Let the common ratio of income is x

A's income = 8x

B's income = 7x

Now the ratio of their expenditure is 19:16

Let the common ratio of expenditure is y

A's expenditure = 19y

B's expenditure = 16y

Savings = income - expenditure

so we have

8x- 19y = 2550 ----(i) and 7x- 16y = 2550 -----(ii)

multiplying (i) by 7 and (ii) by 8 we get

56x-133y = 17850 ----(iii)  and  56x- 128y = 20400 ----(iv)

Now  Subtract (iv) from (iii)

$56x- 133y-( 56x- 128y)=17850-20400\\\\\Rightarrow -133y+128y = -2550\\\\\Rightarrow -5y= -2550\\\\\Rightarrow y= 510$

Now put y = 510 in (i)

$8x-19\times 510= 2550 \\\\\x= 1530$

A's income = 8x = 8 x 1530 = Rs.12240

B's income = 7x= 7 x 1530 =Rs. 10710

Hence, A's income  is Rs.12240 and B's income is Rs. 10710

Answer 2

Let x be the common ratio of income..

So,

A's income is 8x

B's income is 7x

Now,

Let the common ratio of expenditure be y

So,

A's expenditure is 19y

B's expenditure is 16y

As we know,

Savings = Income-Expenditure

so,

A's savings =>8x-19y=2550.........i

B's savings =>7x-16y=2550.........ii

Multiplying equation i by 7 and equation ii by 8.Then subtracting ii from i.

56x-133y=17850

56x-128y=2040

(-) (+) (-)

___________

-5y=-2550

y=510

put the value of y in i, we get..

8x-19×510=2550

=1530

Therefore,

A's income =8x=8×1530=Rupees 12240

B's income =7x=7×1530=Rupees 10710...

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