Question

The ratio of two numbers is 8: 5. If 8 is added to the greater number and 5 is
subtracted from the smaller number, the greater number becomes twice the
smaller number. Find the smaller number,
(1) 15 (2) 75 (3) 25 (4) 45
x varies inversely as y. When x​

Answer 1

Answer :

(4) 45

Explanation :

Ratio of two numbers is 8 : 5

Adding 8 to the greater and subtracting 5 from the smaller number, the greater number becomes 2× of the smaller number.

Find the smaller number.

Let's assume,

• the smaller number = $5x$
• And, greater number = $8x$

Adding 8 to $8x$

$= 8x + 8$

And also, subtract 5 from $5x$

$= 5x - 5$

According to the question,

$\implies \: 8x + 8 = 2 \times (5x - 5)$

$\implies \: 8x + 8 = 10x - 10$

$\implies \: 8 + 10 = 10x - 8x$

$\implies \: 18 = 2x$

$\implies \: \dfrac{18}{2} = x$

$\implies \: 9 = x$

$\underline{ \sf{ \therefore \: The \: value \: of \: \boldsymbol{x} \: is \: 9}}$

Hence, the smaller number is,

• $\boldsymbol{5x = 5(9) = 45}$