Question

what number must be subtrect from each term of the ratio 15:33 so that the ratio become 2:5​

Answer 1

Given:

Ratio = 15:33

To be found:

The number that must be subtracted from each term of the given ratio and will become 2:5

So,

Let the number be x.

$\implies \frac{15 - x}{33-x} = \frac{2}{5}$

[∵ By cross multiplication ]

$\implies 5(15 - x) = 2(33 - x)$

$\implies 5(15) - 5 (x) = 2(33) - 2(x)$

$\implies 75 - 5x = 66 - 2x$

$\implies 75 - 66 = 5x - 2x$

[ ∵ Taking 66 to LHS and (-5x) to RHS ]

$\implies 9 = 3x$

$\implies \frac{9}{3} = x$

$\implies \boxed{x = 3}$

Hence,

3 must be subtracted from each term of the ratio 15:33 so that the ratio becomes 2:5.

.

VERIFICATION:

$LHS = \frac{15-3}{33-3}$

$= \frac{12}{30}$

[Both are divisible by 6]

$= \frac{12}{30} \div \frac{6}{6} = \frac{2}{5} = RHS$

Hence, verified