Ratio of the incomes of A, B and C last year was 3 : 4 : 5. The ratio

1.	Ratio of the incomes of A, B and C last year was 3 : 4 : 5. The ratio of their individual incomes of the last year and this year are 4 : 5, 2 : 3 and 3 : 4 respectively. If the sum of their present incomes is Rs 78800, then find the present individual income of A, B and C. (a) Rs 10000, Rs 40000, Rs 28800 (b) Rs 18000, Rs 28800, Rs 32000 (c) Rs 45000, Rs 12800, Rs 21000 (d) Rs 20000, Rs 14600, Rs 44200
Answer» (b) Rs 18000, Rs 28800, Rs 32000 Let the incomes of A, B and C last year be Rs 3x, Rs 4x and Rs 5x respectively. A’s income last year : this year = 4 : 5 ∴ A’s income this year = \(\frac54\times\) Rs 3x = Rs \(\frac{15x}{4}\) B’s income last year : this year = 2 : 3 ∴ B’s income this year = \(\frac23\times\) Rs 4x = Rs 6x C’s income last year : this year = 3 : 4 ∴ C’s income this year = \(\frac43\times\) Rs 5x = Rs \(\frac{20x}{3}\) ∴ Ratio of present incomes of A, B, C = \(\frac{15x}{4}\) : 6x : \(\frac{20x}{3}\) = \(\frac{15x\times12}{4}:6x\times12:\frac{20x\times12}{3}\) = 45 : 75 : 80 Given, 45x + 72x + 80x = 78800 ⇒ 197x = 78800 ⇒ x = \(\frac{78800}{197}\) = 400 ∴ A’s present income = 45 × 400 = Rs 18000 B’s present income = 72 × 400 = Rs 28800 C’s present income = 80 × 400 = Rs 32000

Ratio of the incomes of A, B and C last year was 3 : 4 : 5. The ratio of their individual incomes of the last year and this year are 4 : 5, 2 : 3 and 3 : 4 respectively. If the sum of their present incomes is Rs 78800, then find the present individual income of A, B and C. (a) Rs 10000, Rs 40000, Rs 28800 (b) Rs 18000, Rs 28800, Rs 32000 (c) Rs 45000, Rs 12800, Rs 21000 (d) Rs 20000, Rs 14600, Rs 44200

Answer»

(b) Rs 18000, Rs 28800, Rs 32000

Let the incomes of A, B and C last year be Rs 3x, Rs 4x and Rs 5x respectively.

A’s income last year : this year = 4 : 5

∴ A’s income this year = \(\frac54\times\) Rs 3x = Rs \(\frac{15x}{4}\)

B’s income last year : this year = 2 : 3

∴ B’s income this year = \(\frac23\times\) Rs 4x = Rs 6x

C’s income last year : this year = 3 : 4

∴ C’s income this year = \(\frac43\times\) Rs 5x = Rs \(\frac{20x}{3}\)

∴ Ratio of present incomes of A, B, C

= \(\frac{15x}{4}\) : 6x : \(\frac{20x}{3}\)

= \(\frac{15x\times12}{4}:6x\times12:\frac{20x\times12}{3}\)

= 45 : 75 : 80

Given, 45x + 72x + 80x = 78800

⇒ 197x = 78800 ⇒ x = \(\frac{78800}{197}\) = 400

∴ A’s present income = 45 × 400 = Rs 18000

B’s present income = 72 × 400 = Rs 28800

C’s present income = 80 × 400 = Rs 32000