Ratios & Proportion

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The monthly incomes of $A$ and $B$ are in the ratio $4 : 5$, their expenses are in the ratio 5 : 6. If '$A$' saves Rs.25 per month and '$B$' saves Rs.50 per month, what are their respective incomes?


Rs.400 and Rs.500


Rs.240 and Rs.300


Rs.320 and Rs.400


Rs.440 and Rs.550

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Option(A) is correct

Let $A$'s income be = $4x$

$A$'s expenses, therefore = $4x–25$

Let $B$'s income be = $5x$

$B$'s expenses, therefore = $5x–50$

We know that the ratio of their expenses = $5:6$

$⇒ 24x−150=25x−250$

$⇒$ Therefore, $x=100$.

$⇒ A$'s income =$4x= 400$ and B's income =$5x= 500$.

Edit: Check out an alternative method using simultaneous equations by Krishna.

(3) Comment(s)


4:5 cross multiply with 5:6 and substract i.e. 25-24= 1

now cross multiply 5:6 with their savings i.e. 25 and 50, therefore


so, 1=100

therefore, their income is, a=4*100=400 and b=5*100=500


This problem can be solved using simultaneous equations,

$4x-5y=25$; $5x-6y=50$;

Solving above equations we get, $x=100$;


is it wrong answer?