Question

two numbers are in the ratio 5:6. when 2 is added to first and 3 is added to second, they are in the ratio 4:5 find the number
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Answer 1

given two numbers in the ratio 5 : 6

let the numbers be 5x and 6x Respectively.

ATQ, when 2 is added to first and 3 is added to second, the ratio become 4 : 5

➡ (5x + 2)/(6x + 3) = 4/5

cross multiplying,

➡ 5(5x + 2) = 4(6x + 3)

➡ 25x + 10 = 24x + 12

➡ 25x - 24x = 12 - 10

➡ x = 2

hence, the numbers are :-

• 5x = 5 × 2 = 10

and

• 6x = 6 × 2 = 12

Answer 2

Let the common ratio be x.

Then the two numbers are 5x and 6x.

If it become (5x+2) and (6x+3), then their ratio becomes 4:5

Therefore,

$\frac{5x + 2}{6x + 3} = \frac{4}{5}$

or, x = 2

So, the numbers are 10 and 12