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If $a : b = 2 : 5,$ then what is the value of $3 a + 2 b 4 a + b ?$

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1613

1316

2522

2021

answer is A.

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Detailed Solution

Given,

a : b = 2 : 5

Using cross multiplication,

⇒ a b = 25

Assuming

a = 2 x

and

b = 5 x

3 a + 2 b 4 a + b = 3 × 2 x + 2 × 5 x 4 × 2 x + 5 x

⇒ 3 a + 2 b 4 a + b = 6 x + 10 x 8 x + 5 x

⇒ 3 a + 2 b 4 a + b = 16 x 13 x

⇒ 3 a + 2 b 4 a + b = 1613

Thus,

3 a + 2 b 4 a + b = 1613

.
Therefore, option 1 is correct.

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