Question

Present age of A is equal to
B's age four years ago. The
respective ratio between the
present ages of A and C is 6 :
5. If B is 8 years older than
C, what is B's present age ?
(in years)
(1) 20 (2) 24
(8) 28
(4) 32
(5) 26​

Answer 1

Assume :

• Let present age of A be "x" years.
• Present age of B be "y" years.
• And present age of C be "z" years.

Solution :

Present age of A is equal to B's age after four years.

According to question,

=> x = y - 4 ___ (eq 1)

Given :

• Ratio of present ages of A and C is 6:5.

=> x/z = 6/5

=> x = 6z/5 ___ (eq 2)

As said in the question,

B is 8 years older than C.

=> y = z + 8 ____ (eq 3)

Substitute value of y in (eq 1)

=> x = z + 8 - 4

=> x = z + 4

=> 6z/5 = z + 4

=> 6z/5 - z = 4

=> (6z - 5z)/5 = 4

=> z = 20 years

Substitute value of z in (eq 3)

=> y = 20 + 8

=> y = 28 years

Substitute value of y in (eq 1)

=> x = 28 - 4

=> x = 24 years

∴ Present age of B is 28 years.

Answer :

Option 3) 28

Answer 2

$\huge\bf{Answer:-}$

The present age of B = 28 years.

Further Explanation

• Let (x) be the present age of A.

• Let (y) be the present age of B.

• Let (z) be the present age of C.

According to the given question:-

• Present age of A is equal to B's age four years ago.The respective ratio between the present ages of A and C is 6 : 5.

• We have to find thewhat is B's present age.

So,

A and C is 6:5 is the present ages.

$\bf(x = y - 4)......equation - (1)$

$\bf \frac{x}{z} = \frac{6}{5}$

$x = \frac{6z}{5} ..........equation - (2)$

$\bf(y = z + 8).........equation - (3)$

Adding values for (y) in equation (1)

$\sf(x = z + 8 - 4) \\ \sf (x = z + 4) \\ \sf( \frac{6z}{5} = z + 4) \\ ( \frac{6z}{5} - z = 4)$

$\sf = > \frac{(6z - 5z)}{5} = 4$

$\sf (z = 20 \: years)$

Adding values for (z) in equation (3)

$\huge\bf(x = 28 - 4) \\ \huge\sf (x = 24 \: years)$

Therefore , The present age of B = 28 years.