Question

A, B and C spend 70%, 75% and 80% respectively of their salaries. Their actual savings are in the ratio 4 : 5 : 6. What is the ratio of their salaries?

(a) 4 : 5 : 6

(b) 4 : 6 : 9

(c) 6 : 5 : 4

(d) 9 : 6 : 4

Answer 1

Correct option is (b) 4 : 6 : 9

We take their incomes as x, y and z.

The expenses of A = 70%,

i.e., The savings of A = (100 − 70)% = 30% = \(\frac{30x}{100}\),

The expenses of B = 75%,

i.e., The savings of B = (100 − 75)% = 25% = \(\frac{25 y}{100}\),

The expenses of C =80%,

i.e., The savings of C = (100 − 80)% = 20% = \(\frac{20 z}{100}\).

By the given condition, we get

\(\frac{30x}{100} : \frac{25 y}{100} : \frac{20z}{100} = 4 : 5 : 6\)

⇒ \(\frac{30 x}{100} = 4\)

⇒ \(x = \frac{40}3\)

⇒ \(\frac{25 y}{100} = 5\)

⇒ \(y = 20\)

⇒ \(\frac{20x}{100} = 6\)

⇒ \(z = 30\)

Therefore x : y : z = \(\frac{40}3 \) : 20 : 30 = 4 : 6 : 9.