If decreasing 110 by x% gives the same result as increasing 50 by x%,

1.	If decreasing 110 by x% gives the same result as increasing 50 by x%, then x% of 650 is what percentage (correct to the nearest integer) more than (x - 10)% of 780 ?1. 12%2. 17%3. 14%4. 18%
Answer» Correct Answer - Option 3 : 14% Given: Decreasing 110 by x% gives the same result as increasing 50 by x%. Calculations: 110 × (100 - x)/100 = 50 × (100 + x)/100 ⇒ 11 × (100 - x) = 5 × (100 + x) ⇒ 1100 - 11x = 500 + 5x ⇒ 16x = 600 ⇒ x = 600/16 ⇒ x = 37.5 x% of 650 = 37.5% × 650 ⇒ 243.75 (x - 10)% of 780 = (37.5 - 10)% × 780 ⇒ 27.5% × 780 ⇒ 214.50 Percentage difference = {(243.75 - 214.50)/214.50} × 100 ⇒ (29.25/214.50) × 100 ⇒ 13.63% ≈ 14% ∴ x% of 650 is 14% more than (x - 10)% of 780.

If decreasing 110 by x% gives the same result as increasing 50 by x%, then x% of 650 is what percentage (correct to the nearest integer) more than (x - 10)% of 780 ?1. 12%2. 17%3. 14%4. 18%

Answer» Correct Answer - Option 3 : 14%

Given:

Decreasing 110 by x% gives the same result as increasing 50 by x%.

Calculations:

110 × (100 - x)/100 = 50 × (100 + x)/100

⇒ 11 × (100 - x) = 5 × (100 + x)

⇒ 1100 - 11x = 500 + 5x

⇒ 16x = 600

⇒ x = 600/16

⇒ x = 37.5

x% of 650 = 37.5% × 650

⇒ 243.75

(x - 10)% of 780 = (37.5 - 10)% × 780

⇒ 27.5% × 780

⇒ 214.50

Percentage difference = {(243.75 - 214.50)/214.50} × 100

⇒ (29.25/214.50) × 100

⇒ 13.63% ≈ 14%

∴ x% of 650 is 14% more than (x - 10)% of 780.

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If decreasing 110 by x% gives the same result as increasing 50 by x%, then x% of 650 is what percentage (correct to the nearest integer) more than (x - 10)% of 780 ?1. 12%2. 17%3. 14%4. 18%

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