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60 percent of a smaller number is 16 less than 40 percent of a larger number. If the sum of both the numbers is 120, then what is the difference between the larger number and the smaller number?

60 percent of a smaller number is 16 less than 40 percent of a larger number. If the sum of both the numbers is 120, then what is the difference between the larger number and the smaller number? Correct Answer 56

Given:

The sum of the larger and smaller number = 120

Formula used:

GM% = (GM/TM) × 100

Where, GM = Gain marks, and TM = Total marks

Calculation:

Let be assume the larger number is L and the smaller number is S

⇒ S × (60/100) = (40/100) × L - 16

⇒ 0.60S = 0.40L - 16

⇒ 4L - 6S = 160 ....... (1)

⇒ L + S = 120 ....... (2)

By solving (1) and (2)

⇒ L = 88 and S = 32

⇒ L - S = 88 - 32 = 56

∴ The required result will be 56.

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