Question

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 are the original angles respectively?40∘ and 70∘ 30∘ and 70∘ 30∘ and 60∘ 40∘ and 60∘

Solution

The correct option is A 40∘ and 70∘ The ratio of the angles = 4: 7 ∴ Let the angles be 4x and 7x. Adding10∘ to the smaller angle and subtracting 20∘ to the larger angle,  ⇒ he smaller angle = 4x + 10∘  and final value of larger angle = 7x - 20∘- The angles are now in the ratio 1:1 ⇒ 4x + 10∘ = 7x - 20∘ ⇒ 7x-4x = 20∘+10∘ ⇒ 3x = 30∘ ⇒ x = 10∘ ∴ The value of larger angle = 7x = 70∘ and value of smaller angle = 4x = 40∘

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