Question

two numbers are in the ratio 2:5. if each number is increased by 13 , the ratio becomes 5:6. find the sum of this two numbers.​

Answer 1

Step-by-step explanation:

this is your answer please mark me as best and ask more questions that I answer

Answer 2

Given,

Two numbers are in the ratio 2:5. if each number is increased by 13 , the ratio becomes 5:6.

To Find,

The sum of these two numbers.

Solution,

→ Ratio of the original numbers = 2:5

→ Ratio of the numbers when both are increased by 13 = 5:6

→ Let the original numbers be 2x and 5x.

→ We know that,

= 2x + 13 : 5x + 13 = 5:6

[ A ratio can be represented in a fractional form. Hence,]

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

→ Cross-multiplying the values,

= 6 (2x+13) = 5 (5x+13)

[Opening the brackets]

= 12x + 78 = 25x + 65

= 12x - 25x = 65 - 78

= -13x = -13

∴ x = 1

→ Substituting the values for the ratio,

2x = 2 x 1 = 2

5x = 5 x 1 = 5

Therefore, the numbers in the ratio 2:5 are 2 and 5 and their sum is →

2 + 5 = 7

How to Verify?

→ It is given that upon adding 13 to both the numbers in the ratio, the new ratio formed is 5:6.

In equation form,

= $\dfrac{2+13}{5+13}=\dfrac{5}{6}$

= $\dfrac{2+13}{5+13}$ = $\dfrac{15}{18}$

→ Simplifying  $\dfrac{15}{18}$, we get the ratio 5:6.

Hence, verified