Question

Two numbers are in ratio of 3:5 . If 8 is added to each number, the ratio becomes 2:3.find the numbers​

Answer 1

Answer:

Lets call the numbers p and q (for a change)

The first ratio means 5p = 3q

This may look the wrong way round, but remember p is the smaller number so needs the bigger multiplier to become equal

The second Ratio means 3(p+8) = 2(p+8) [using the same logic)

3p + 24 = 2q + 16 [Multiplying out the brackets]

Now we have got two equations, there are different ways to combine them

I’m going to do this by substitution

Simplify the 2nd to give 3p + 8 = 2q and then q = 3/2 * p + 4

(By taking 16 from both sides then dividing by 2)

5p = 3(3/2 * p + 4) = 9/2 + p + 12 - Substituting our statement for q into the first equation)

The 1/2 is a bit awkward so I will multiply through by 2

10p = 9p + 24

Take 9p from both sides

p = 24

Use this value of p and the first ratio

3q = 5 * 24 = 120.

so q = 40

We have a solution now; p=24, q= 40. But I always like to check the answer against the question

p:q = 24:40 = 3:5 - good

(p+8):(q+8) = 32:48 = 2:3 Good

Answer 2

Solution :-

Let's :-

• First number = 3x

• Second number = 5x

According to question if 8 is added to both numbers then the ratio become 2 : 3

$\implies \sf \frac{3x +8}{5x + 8} = \frac{2}{3} \\ \\\implies \sf 3(3x + 8) = 2(5x + 8) \\ \\\implies \sf 9x + 24 = 10x + 16 \\ \\\implies \sf 9x - 10x = 16 - 24 \\ \\\implies \sf - x = - 8 \\ \\ \implies \underline {\boxed{\sf x = 8}}$

Therefore

First number = 3 × 8 = 24

2nd number = 5 × 8 = 40

→ 24 and 40 are the numbers