Question

A's age is 20% more than C but 10% less than B. If D (45 years old) is thrice as old as C, what
is the age of B?​

Answer 1

Answer:

Given, A = 20%C + C [A's age is 20% more than C; Given] ---------- 1

Also given, A = B - 10%B  [A's age is 10% less than B; Given] ---------- 2

D is 45 years old [Given]

Also, D = 3C [Given; D is thrice as old as C]

⇒ 45 = 3C [Putting D's age; which is 45 years]

⇒ C = 45/3

⇒ C = 15 years

Now, Let's calculate eq.1:

20%C + C = A

⇒ 20C / 100 + C = A

⇒ C/5 + C = A

⇒ $\frac{C + 5C}{5}$ = A

⇒ $\frac{6C}{5}$ = A

⇒ (6 x 15) / 5 = A [Substituting C with its age we found out above; 15 years]

⇒ 18 = A

⇒ A = 18 years

Now, putting the value of A in eq.2:

⇒ B - 10%B = 18

⇒ B - 10B / 100 = 18

⇒ B - B/10 = 18

⇒ $\frac{10B - B}{10}$ = 18

⇒ $\frac{9B}{10}$ = 18

⇒ 9B = 180

⇒ B = 180/9 = 20

⇒ B = 20 years

Therefore, age of B is 20 years

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