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If two numbers are in ratio 5 ∶ 6. If first number is increased by 65% and the second number is increased by 40%, the sum of the new numbers is 333. Find the original numbers?


1. 100, 120
2. 90, 108
3. 105, 126
4. 120, 144

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Correct Answer - Option 1 : 100, 120

Given:

The ratio of original number = 5 ∶ 6

New 1st number = 165% of original 1st number

New 2nd number = 140% of the original 2nd number

Sum of the new number = 333

Calculation:

Let the original number be 5x and 6x.

New 1st number = 165% of 5x

New 2nd number = 140% of 6x

Sum of the new number = 333

⇒ 165% of 5x + 140% of 6x = 333

⇒ 825x/100 + 840x/100 = 333

⇒ 8.25x + 8.4x = 333

⇒ 16.65x = 333

⇒ x = 333/16.65

⇒ x = 20

Original 1st number = 5x

⇒ Original 1st number = 100

Original 2nd number = 6x

⇒ Original 2nd number = 120

The original numbers are 100 and 120.

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