Question

Mark (✓) against the correct answer
Two numbers are in the ratio 3 : 5. If each number is increased by 10, the ratio becomes 5 : 7. The sum of the numbers is

(a) 8
(b) 16
(c) 35
(d) 40

Answer 1

(d) 40

Suppose that the numbers are x and y.

Then, x : y = 3 : 5 and (x + 10) : (y + 10) = 5 : 7

$$\begin{gathered} \frac{x}{y}=\frac{3}{5} \\ x=\frac{3y}{5} \\ =>\frac{x+10}{y+10}=\frac{5}{7}=>7x+70=5y+50=>7\times \frac{3y}{5}+70=5y+50=>5y-\frac{21y}{5}=20=>\frac{4y}{5}=20=>y=25\mathrm{Therefore},x=\frac{3\times 25}{5}=15 \end{gathered}$$

Hence, sum of numbers = 15 + 25 = 40