Question

Ratio of 2 number is 2:3.If 5 is added to both of the number, then we get new ratio 4:5, find the smaller number.​

Answer 1

Answer -

• The smaller number = 5.

To find -

• The smaller number.

Step-by-step explanation -

Let the numbers be "2x" and "3x" respectively, as they are in the ratio 2 : 3.

Adding 5 to both the numbers -

• The first number becomes "2x + 5".
• The second number becomes "3x + 5".

Given that -

• When 5 is added to both the numbers, we get the new ratio as 4 : 5.

Therefore -

$\longmapsto \bf \dfrac{2x + 5}{3x + 5} = \dfrac{4}{5}$

$\bf\longmapsto 4 \: (3x + 5) = 5 \: (2x + 5)$

$\longmapsto \bf 12x + 20 = 10x + 25$

$\longmapsto \bf12x - 10x = 25 - 20$

$\longmapsto \bf2x = 5$

$\longmapsto \bf x = \cancel{\dfrac{5}{2}}$

$\longmapsto \bf x = 2.5$

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Hence, the numbers are -

$\sf2x = 2 \times 2.5 = 5$

$\sf3x = 3 \times 2.5 = 7.5$

And -

• The smaller number is 5.

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