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The ratio of income of two persons is $9 : 7$ and the ratio of their expenditure is $4 : 3$ . If each of them manages to save Rs. $2000$ per month, find their monthly income.

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Rs . 18, 000, Rs . 14, 000

Rs . 1, 000, Rs . 14, 000

Rs . 18, 000, Rs . 1, 000

None of these

answer is A.

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Detailed Solution

Given the ratio of income of two persons is

9 : 7

and the ratio of their expenditure is

4 : 3

and each of them manages to save Rs.

2000

per month.
Let their salaries be

9 x

and

7 x

.
Let their expenditure be

4 y

and

3 y

.
According to the question,

9 x - 4 y = 2000

……………..

(1)

7 x - 3 y = 2000

……………..

(2)

.
From

(1),

we get,

x = \frac{2000 + 4 y}{9}

………………..

(3)

On putting

x

as an expression of y getting form (3) in

(2)

we get,

7 \times \frac{(2000 + 4 y)}{9} - 3 y = 2000

\Rightarrow

\frac{(14000 + 28 y)}{9} - 3 y = 2000

\Rightarrow \frac{14000 + 28 y - 27 y}{9} = 2000

\Rightarrow

14000 + y = 18000

\Rightarrow

y = 4000

Now, putting

y = 4000

in (3) we get,

x = \frac{2000 + 4 \times 4000}{9}

\Rightarrow

x = \frac{2000 + 16000}{9}

\Rightarrow

x = \frac{18000}{9}

\Rightarrow

x

= 2000

So, salary of first person

= 9 \times 2000 = Rs . 18000

and
salary of second person

= 7 \times 2000 = Rs . 14000

.
Hence, this is the answer.
So the correct option 1.

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