The incomes of two persons 𝐴 and 𝐵 are in the ratio 8: 7, the ratio of their expenditures is 19: 16. If they save rupees 2550 per month, what is their monthly income?

We are given that the income of two persons is in the ratio 8: 7. Let the income of

𝐴 and 𝐵 be 8𝑥 and 7𝑥, respectively.

Their expenditures are in the ratio 19: 16. Let them be 19𝑦 and 16𝑦, respectively. And each of them saves rupees 2550 per month.

Now, the difference between income and expenditure gives the amount of savings.

So, for person 𝐴, 8𝑥 − 19𝑦 = 2550
And for person 𝐵, 7𝑥 − 16𝑦 = 2550
As the RHS of both equations are the same, so equating the LHS parts, we get
8𝑥 − 19𝑦 = 7𝑥 − 16𝑦                        ......eq(1)
⇒ 8𝑥 − 7𝑥 =− 16𝑦 + 19𝑦               ........eq(2)
⇒ 𝑥 = 3𝑦       ................. eq(3)
Putting this value of 𝑥 in eq(2), we get
7 × 3𝑦 − 16𝑦 = 2550
⇒ 21𝑦 − 16𝑦 = 2550
⇒ 5𝑦 = 2550
⇒ 𝑦 = 2550  
⇒ 𝑦 = 510
Now, putting the value of 𝑦 in eq(3), we get
𝑥 = 3 × 510
⇒ 𝑥 = 1530
The monthly income of 𝐴 is = 8𝑥
= 8 × 1530
= 12240
The monthly income of 𝐵 is = 7𝑥
= 7 × 1530

= 10710
Hence, the monthly income of 𝐴 and 𝐵 are rupees 12240 and rupees 10710, respectively.