Question

Two angles are in the ratio 4: 7. On incresing the smaller angle by 10${}^{\circ }$ and decreasing the larger angle by 20${}^{\circ }$ the ratio of the angles becomes 1:1. The original angles were ___ and ____respectively.

• A. 40${}^{\circ }$ and 70${}^{\circ }$
• B. 30${}^{\circ }$ and 70${}^{\circ }$
• C. 30${}^{\circ }$ and 60${}^{\circ }$
• D. 40${}^{\circ }$ and 60${}^{\circ }$

Answer 1

The correct option is A

40${}^{\circ }$ and 70${}^{\circ }$

The ratio of the angles = 4: 7

$\therefore$ Let the angles be 4$x$ and 7$x$.

Adding10${}^{\circ }$ to the smaller angle and subtracting 20${}^{\circ }$ from the larger angle, we get

$\Rightarrow$ The smaller angle = 4$x$ + 10${}^{\circ }$

and the final value of the larger angle = 7$x$ - 20${}^{\circ }$

The angles are now in the ratio 1:1

$\Rightarrow$ 4$x$ + 10${}^{\circ }$ = 7$x$ - 20${}^{\circ }$

$\Rightarrow$ 7$x$-4$x$ = 20${}^{\circ }$+10${}^{\circ }$

$\Rightarrow$ 3$x$ = 30${}^{\circ }$

$\Rightarrow$ $x$ = 10${}^{\circ }$

$\therefore$ The value of the larger angle = 7$x$

= 70${}^{\circ }$

and the value of the smaller angle = 4$x$

= 40${}^{\circ }$