Question

The sum of the ages of A and B is four-thirds the
age of C. The age of B.is two-thirds the age of C.
If the sum of the ages of the three persons is
35 years, find the age of B.​

Answer 1

Age of B = 10 years.

Solution :-

Given :-

$\sf (i) \: A \: + \: B \: = \frac{4}{3} C \\ \sf (ii) \: B \: = \frac{2}{3} C \\ \sf (iii) \: A \: + \: B \: + \: C \: = 35$

Substituting value of (i) in (iii),

$\rightarrow \sf \frac{4}{3} C \: + \: C = 35 \\ \rightarrow \sf \: \frac{4C + 3C}{3} = 35 \\ \rightarrow \sf \: \frac{7C}{3} = 35 \\ \rightarrow \sf \: 7C = 105 \\ \rightarrow \sf \: C \: = \frac{105}{7} \\ \rightarrow \sf \: C \: = 15$

Substituting value of C in (ii),

$\sf \: B \: = \: \frac{2}{3} C \\ \sf \: B \: = \frac{2}{3} \times 15 \\ \sf \: B \: = 2 \times 5 \\ \sf \: B \: = 10$

Answer 2

Answer:

Age of B is 10yrs .

Step-by-step explanation:

Given :

A + B = 4/3 C ................(1)

B = 2/3 C ........................(2)

A + B + C = 35 ..............(3)

Substituting value of (i) in (iii)

A + B + C = 35

4/3 C + C = 35

(4C + 3C)/3 = 35

7C/3 = 35

7C = 105

C = 105/7 = 15

Now,

From eq. (2)

B = 2/3 C

= 2/3 × 15

= 10

Hence,

Age of B is 10 yrs .

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