Aptitude Discussion

Q. |
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? |

✔ A. |
Rs.400 and Rs.500 |

✖ B. |
Rs.240 and Rs.300 |

✖ C. |
Rs.320 and Rs.400 |

✖ D. |
Rs.440 and Rs.550 |

**Solution:**

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.**

**Xyz**

*()
*

**Krishna**

*()
*

This problem can be solved using simultaneous equations,

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

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

**Sandeep**

*()
*

is it wrong answer?

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

250-150=100

so, 1=100

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