Question

Two angles are in the ratio 1: 2. On increasing the smaller angle by 6 and decreasing thelarger angle by 6, the ratio changed to 2:3.What were the original angles ?​

Answer 1

Answer:

Let the two angles be x and 2x

Increasing smaller by 6° and decreasing the larger by 6°, the ratio changes to 2: 3

⇒

⇒ 3×(x + 6) = 2×(2x – 6)

⇒ 3x + 18 = 4x – 12

⇒ 4x – 3x = 18 + 12

⇒ x = 30

Original angles are 30° and 2x = 2× 30 = 60°

∴ Original angles are 30° and 60°

Answer 2

Given

• Two angles are in the ratio 1: 2

To find

• Original angles

Let,

• Smaller Angle be x
• Larger angle be 2x

It is given that on increasing the smaller angle by 6 and decreasing the larger angle by 6 then, Ratio Changed to 2:3

According to Question

$\\→ \sf \cfrac{x + 6}{2x - 6} = \cfrac{2}{3}$

Cross Multiplying Both side

$\\→ \sf 3(x + 6) = 2(2x - 6)$

$\sf→ 3x + 18 = 4x - 12$

On transfering 4x to LHS and 18 to RHS

$\\\sf→ 3x - 4x = - 12 - 18$

$\sf → - x = - 30$

$\sf → x = 30$

• The Original angel are 30 and 60.

Verification

$\dfrac{30}{60} = \dfrac{1}{2}$

$\dfrac{1}{2} = \dfrac{1}{2}$

Verified