If a:b=2:3 then (5a-2b): (5a+2b) is equal to:Options3 : 71 : 31 : 42 : 7

Given that a:b = 2:3, we can assume a = 2k and b = 3k for some constant k.

We need to find the ratio (5a - 2b) : (5a + 2b).

Substituting the values of a and b, we get:

(5(2k) - 2(3k)) : (5(2k) + 2(3k)) = (10k - 6k) : (10k + 6k) = 4k : 16k.

Simplifying this ratio by dividing both sides by 4k, we get 1 : 4.

So, the ratio (5a - 2b) : (5a + 2b) is 1 : 4. However, this option is not given in the question. There might be a mistake in the question or the options provided.

The given ratio is a:b = 2:3.

We are asked to find the ratio (5a-2b) : (5a+2b).

Let's substitute the given ratio into the expression:

First, substitute a = 2k and b = 3k (where k is a constant) into the expression.

So, (5a-2b) becomes 5(2k) - 2(3k) = 10k - 6k = 4k.

And (5a+2b) becomes 5(2k) + 2(3k) = 10k + 6k = 16k.

Therefore, the ratio (5a-2b) : (5a+2b) becomes 4k : 16k.

Simplify this ratio by dividing both sides by 4k, we get 1 : 4.

So, the answer is 1 : 4.