# 75% of a number is added to 75. If half of the initial number is subtracted from the resulting number to arrive at final result equal to 110, find the

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75% of a number is added to 75. If half of the initial number is subtracted from the resulting number to arrive at final result equal to 110, find the original number.

1. 100
2. 150
3. 140
4. 120

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Correct Answer - Option 3 : 140

Given:

75% of a number is added to 75.

half of number is subtracted from the resulting number to arrive at final result equal to 110.

Concepts used:

Resulting number = 75% of original number + 75

Calculation:

75% of a number is added to 75.

Let original number be equal to x.

⇒ Resulting number = 75% of original number + 75

⇒ Resulting number = 0.75x + 75

half of number is subtracted from the resulting number to arrive at final result equal to 110.

⇒ New final number = 0.75x + 75 – 0.50x = 0.25x + 75

⇒ 110 = 0.25x + 75

⇒ 110 – 75 = 0.25x

⇒ x = 140

∴ Original number is equal to 140.