Question

The ages of two friends are in the ratio 6 : 5 if sum of their ages is 66. After how many years the ratio will become 7 : 6? Select one:

a. 6

b. 10

c. 12

d. 11

Answer 1

Answer:

After 6 years, the ratio of ages of friends will become 7 : 6

Step-by-step explanation:

Let the two friends be a and b

Present age of a be $6x$ years

Present age of b be $5x$ years

Given that sum of their ages is 66

Thus, we get

$6x + 5x = 66\\\\ 11x = 66\\\\ x = \frac{66}{11}\\\\ x = 6$

Thus, present age of a $= 6 \times 6 = 36$ years

Present age of b $= 5 \times 6 = 30$ years

Let after $z$ years, the ratio becomes 7 : 6

After $z$ years

Age of a $= 36 + x$ years

Age of b $= 30 + x$ years

Now, we get

$\frac{36 + x}{30 + x} = \frac{7}{6}\\\\ 6 \times (\,36 + x)\, = 7 \times (\,30 + x)\,\\\\ 216 + 6x = 210 + 7x\\\\ 7x - 6x = 216 - 210\\\\x = 6$

Thus, after 6 years, the ratio of ages of friends will become 7 : 6