Question

The monthly salaries of two persons are in the ratio 6:10. If each receives an increase of rs. 400 in monthly salaries the new ratio is 13:21. Find their original salaries.

Answer 1

Answer

Let the salary of first person be 6y.

Let the salary of second person be 10y.

According to the question,

$\sf \dashrightarrow 6 : 10 + 400 : 400 = 13 : 21$

$\sf \dashrightarrow \dfrac{6x + 400}{10x + 400} = \dfrac{13}{21}$

Cross multiply the numbers.

$\sf \dashrightarrow 21 (6x + 400) = 13 (10x + 400)$

$\sf \dashrightarrow 126x + 8400 = 130x + 5200$

$\sf \dashrightarrow 126x - 130x = 5200 - 8400$

$\sf \dashrightarrow -4x = -3200$

$\sf \dashrightarrow x = \dfrac{-3200}{-4}$

$\sf \dashrightarrow x = 800$

Now, we can find the original salaries of both persons.

Original salary of first person :

$\sf \dashrightarrow 6x = 6(800)$

$\sf \dashrightarrow Rs.4800$

Original salary of second person :

$\sf \dashrightarrow 10x = 10(800)$

$\sf \dashrightarrow Rs.8000$

Hence, the salary of first and second person are ₹4800 and ₹8000 respectively.