Two angles are in the ratio 4 - 7- On increasing the smaller angle by 10- and decreasing the larger angle by 20- the ratio of the angles becomes 1 - 1- What is the value of the original smaller angle-

The ratio of the angles = 4: 7 ∴ Let the angles be 4x and 7x. Adding 10^∘ to the smaller angle and subtracting 20^∘ from nbsp;the larger angle. ⇒Final valu ...

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Standard VIII

Mathematics

Increasing or Decreasing a Ratio

Two angles ar...

Question

Two angles are in the ratio 4 : 7. On increasing the smaller angle by $10^{\circ}$ and decreasing the larger angle by $20^{\circ},$ the ratio of the angles becomes 1 : 1. What is the value of the original smaller angle?
40

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Solution

The correct option is A 40
The ratio of the angles = 4: 7

$∴$ Let the angles be $4 x$ and $7 x$ .

Adding 10 $^{\circ}$ to the smaller angle and subtracting 20 $^{\circ}$ from the larger angle.

$\Rightarrow$ Final values of
Smaller angle = $4 x + 10^{\circ}$ and

Larger angle = $7 x - 20^{\circ}$

The angles are now in the ratio 1 : 1

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

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

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

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

$∴$ The value of smaller angle
$= 4 x = 40^{\circ}$

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Two angles are in the ratio 4 : 7. On increasing the smaller angle by 10∘ and decreasing the larger angle by 20∘, the ratio of the angles becomes 1 : 1. What is the value of the original smaller angle?40

Two angles are in the ratio 4 : 7. On increasing the smaller angle by $10^{\circ}$ and decreasing the larger angle by $20^{\circ},$ the ratio of the angles becomes 1 : 1. What is the value of the original smaller angle?
40