CAT 2022 Slot 1 Paper

Question : 55 of 66

Marks: +1, -0

Let $a$ and $b$ be natural numbers. If $a^2 +ab + a=14$ and $b^2 +ab + b=28$ , then $(2a+b)$ equals

Solution:

a(a+b+1)=14

...(i)

b(a+b+1)=28

...(ii)

{a}/{b}=\;{1}/{2}

b=2 a

Substituting in

(i)

, we get

a(3 a+1)=14

3 a^2+a-14=0

3 a^2-6 a+7 a-14=0

3 a(a-2)+7(a-2)=0

Given,

a

and

b

are natural numbers.
Therefore,

a=2

and

b=4

2 a+b=2(2)+4=8

The answer is option A.

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