NIFT PG 2020 Question Paper with solutions

Question : 15 of 150

Marks: +1, -0

If the arithmetic mean of

3 a

and

4 b

is greater than 50 , and

a

is twice

b

, then the smallest possible integer value of

a

Solution:

Let

b=x

∴ \;\; a=2 x

According to the question,

\;{3 a+4 b}/{2}>50

⇒ \;\; 3 a+4 b>100

⇒ \;\; 6 x+4 x>100

[ ∵ a=2 x

and

b=x]

⇒ 10 x>100

⇒ x > 10

⇒2 x > 20

⇒ a > 20

Thus, the smallest possible integer value of

a

is 21 .

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