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

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Rs 18000, Rs 14, 000

Rs 10, 000, Rs 13, 000

Rs 16, 000, Rs 11, 000

None of these

answer is A.

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Detailed Solution

Given
Income Ratio two persons

= 9 : 7

= 9 k_{1} : 7 k_{1}

Here,

k_{1} =

constant of proportionality
Now, ratio of expenditure

= 4 : 3

= 4 k_{2} : 3 k_{2}

We know,

saving is the difference of income and

expe nditure

. Both saves

Rs 2000

per month. Thus, for person 1,

2000 = 9 k_{1} - 4 k_{2}

For person 2

2000 = 7 k_{1} - 3 k_{2}

Suppose

9 k_{1} - 4 k_{2} = 2000 . . . . . (1)

7 k_{1} - 3 k_{2} = 2000 . . . . . . (2)

Subtract equation number

(2)

from equation

(1)

, we get,

2 k_{1} - k_{2} = 0 \Rightarrow 2 k_{1} = k_{2}

Put the value of

k_{2}

(1)

, we get

\Rightarrow 9 k_{1} - 4 (2 k_{1}) = 2000 \Rightarrow 9 k_{1} - 8 k_{1} = 2000 \Rightarrow k_{1} = 2000

So, person 1 income is,

\Rightarrow 9 k_{1}

= 9 \times 2000

= Rs 18, 000

Person 2 income is,

\Rightarrow 7 k_{1}

= 7 \times 2000

= Rs 14, 000

Hence, option 1 is correct.

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