NIFT PG 2020 Question Paper with solutions

Question : 27 of 150

Marks: +1, -0

The average age of 30 students of a class is 14 yr 4 months. After admission of 5 new students in the class the average becomes 13 yr 9 months. The youngest one of the five new students is 9 yr 11 months old. The average age of the remaining 4 new students is

13 yr 6 months
12 yr 4 months
10 yr 4 months
11 yr 4 months

Validate

Solution:

Let the average age of 4 new students be

a

∴ 30(14 \;{1}/{3})+9 \;{11}/{12}+4 a=35(13 \;{3}/{4})

⇒ 30 × \;{43}/{3}+\;{119}/{12}+4 a=35 × \;{55}/{4}

⇒ \;\; 430+\;{119}/{12}+4 a=\;{1925}/{4}

⇒ \;\; 4 a=\;{1925}/{4}-\;{119}/{12}-430

⇒ \;\; 4 a=\;{5775-119-5160}/{12}

⇒ \;\; 4 a=\;{496}/{12}

⇒ \;\; a=\;{496}/{48}=\;{31}/{3}=10 \;{1}/{3}

Hence, average age

=a=10

yr 4 months

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