Question

The ratio of monthly incomes of Mr. $X$ and Mr. $Y$ is $3:4$ and the ratio of their monthly expenditures is $5:7$. If the ratio of their monthly savings is $3:2$ and Mr X saves Rs. $500$ more than Mr. $Y$ per month, then find the monthly income of Mr. $Y$ [in Rs. ]

• A. $22000$
• B. $16500$
• C. $11000$
• D. $5500$

Answer 1

The correct option is A $22000$

Given:

Ratio of monthly incomes of $X$ and $Y$ $=3:4$

Ratio of monthly expenditure of $X$ and $Y$ $=5:7$

Ratio of monthly savings of $X$ and $Y$ $=3:2$

Solution:

Suppose

Proportion value of monthly income $=x$

Proportion value of monthly expenditures $=y$

Proportion value of monthly savings $=z$

Hence,

Monthly savings of $X$ $=3z$

Monthly savings of $Y$ $=2z$

According to question,

$3z=2z+500$

or, $z=500$

Savings of $X$ $=3\times 500=1500$

Savings of $Y$ $=2\times 500=1000$

We know that ,

Income - Expenditure = Savings

So, for Mr. $X$

$3x-5y=1500$ $............\left(i\right)$

For Mr. $Y$

$4x-7y=1000$ $...............\left(ii\right)$

Multiplying eqn.(i) by $7$ and eqn.(ii) by $5$ and subtract eqn. (ii )from (i) we get,

$21x-20x=10500-5000$

or, $x=5500$

Putting value of $x=5500$ in eqn (i) we get,

$3\times 5500-5y=1500$

or, $5y=16500-1500=15000$

or, $y=3000$

Income of $Y$ $=4x=4\times 5500=22000$

Hence, income of $Y$ $=Rs.22000$

Therefore, A is the correct option.