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SSC MTS 2023 PYQ — Question 7

SSC MTS - 09 May 2023 - Shift 1 • Quantitative Aptitude • Q7

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The average age of 15 members of a committee is increased by 4 years when two members whose ages are 60 years and 70 years are replaced by two new members. What is the average age of the new members?

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 95 years.

Average = sum of observationsnumber of observations\frac{sum\ of\ observations}{number\ of\ observations}

Let the sum of the ages of the new members be X and the average be A

Sum of 15 old members15=A\frac{Sum\ of\ 15\ old\ members}{15} = A

Now 2 members leave and 2 new join 

Average now = Sum of 15 old members−60−70 + x15\frac{Sum\ of\ 15\ old\ members - 60 - 70 \ +\ x}{15}  = A + 4

A + 4 = 15A−130+x15\frac{15A - 130 + x}{15}

15A + 60 = 15A - 130 + x

x = 190

Hence, the average ages of the 2 new members = 1902=95\frac{190}{2} = 95 years.