Question

2. Two numbers are in the ratio 2:5. If each number is increased by 13, the ratio be
comes 5:6. What is the sum of the number?


please answer with explanation​

Answer 1

Answer:-

Sum of the numbers is 7

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• Given:-

Ratio of the 2 numbers = 2:5

Each number is increased by = 13

New Ratio = 5:6

• To Find:-

The sum of the numbers = ?

• Solution:-

Let the Numbers be 2x and 5x

Hence,

ATQ:-

→ (2x + 13) : (5x + 13) = $\dfrac{5}{6}$

→ $\dfrac{(2x + 13)}{(5x + 13)} = \dfrac{5}{6}$

• Cross Multiplying:-

→ $6 (2x + 13) = 5 (5x + 13)$

→ $12x + 78 = 25x + 65$

→ $12x - 25x = 65 - 78$

→ $-13x = -13$

→ $x = \dfrac{-13}{-13}$

$\implies\bf{x = 1}$

• Putting x = 1 in the Ratio :-

2x → $2 \times 1 \implies\bf{2}$

5x → $5 \times 1 \implies\bf{5}$

Therefore, the two numbers are 2 and 5

Sum of the two numbers is 2 + 5 = 7

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• Verification:-

It is given that the Ratio becomes 5:6 on increasing it by 13.

i.e;

Adding 13 in the Orignal Ratio:-

→ $\dfrac{2 + 13}{5 + 13}$

→ $\dfrac{15}{18}$

• Simplifying:-

→ $\dfrac{5}{6}$

which is equal to the New Ratio.

Hence, Verified

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