If a : b = 3 : 8 then (7a + 2b) : (7a – 2b) is

Correct Answer is : 21:1621 : 1621:16

Correct Answer is : 21:1621 : 1621:16

Test Index

Ratio and Proportion

Question : 1 of 112

Marks: +1, -0

a : b = 3 : 8

(7a + 2b) : (7a – 2b)

Solution:

Concept:

Use a common multiplier

k

to express

a

and

b

from the given ratio, then substitute into the expression.

Explanation:

Given

a : b = 3 : 8

, let

a = 3k

and

b = 8k

, where

k

is a nonzero constant.

Compute

7a + 2b = 7(3k) + 2(8k) = 21k + 16k = 37k

Compute

7a - 2b = 7(3k) - 2(8k) = 21k - 16k = 5k

Thus

(7a + 2b) : (7a - 2b) = 37k : 5k = 37 : 5

Answer:

The required ratio is

37 : 5

, which corresponds to option B.

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