Question

Two numbers are in the ratio 5:7. On adding 1 to the first and 3 to the second, their ratio
becomes 6/9. Find the numbers.​

Answer 1

Solution:

We have to find out the numbers, given that,

• The numbers are in the ratio 5 : 7.
• On adding 1 to the first and 3 to the second, the ratio becomes 6 : 9.

So, let the numbers be 5x an 7x. So, Ratio = 5x/7x = 5 : 7

On adding 1 to first number, we get,

= 5x + 1

On Adding 3 to the second, we get,

= 7x + 3

According to the given condition,

$\tt\implies\dfrac{5x+1}{7x+3}=\dfrac{6}{9}$

$\tt\implies\dfrac{5x+1}{7x+3}=\dfrac{2}{3}$

On Cross Multiplying, we get,

$\tt\implies3(5x+1)=2(7x+3)$

$\tt\implies15x+3=14x+6$

$\tt\implies15x-14x=6-3$

$\tt\implies x=3$

So,

→ 5x = 15

→ 7x = 21

★ Therefore, the numbers are 15 and 21.

Answer:

• The numbers are 15 and 21

•••♪