Question

.Twovnumbers are in the ratio 5:9 .On

subtracting 3 from each ,the ratio becomes1:2 . find the number​

Answer 1

Correct Question:

Two numbers are in the ratio 5 : 9. On subtracting 3 from each, the ratio becomes 1 : 2. Find the number.

Given:

Two ratios:-

• Ratio 1 :- 5 : 9
• Ratio 2 :- 1 : 2

What To Find:

We have to find the numbers.

How To Find:

To find the numbers, we have to,

• Take x as a common multiple in the ratio 5 : 9 = 5x : 9x
• According to the statement the equation will be  $\sf{\dfrac{5x - 3}{9x - 3} = \dfrac{1}{2}}$.
• Solve the equation and substitute the values.

Solution:

$\sf{\dfrac{5x - 3}{9x - 3} = \dfrac{1}{2}}$

Use cross multiplication,

⇒ 2 (5x - 3) = 1 (9x - 3)

Solve the brackets,

⇒ 10x - 6 = 9x - 3

Take 9x to LHS and 6 to RHS,

⇒ 10x - 9x = -3 + 6

Solve the both sides,

⇒ x = 3

Now, substitute the values,

• 5x = 5 × 3 = 15
• 9x = 9 × 3 = 27

∴ Thus, the two numbers are 15 and 27.