Question

ratio of present age of A B and C is 4:6:7 respectively after 8 years ratio of age of a two age of B is 5:7 find the present age of c​

Answer 1

Correct Question:

• The ratio of present age of A, B and C is 4 : 6 : 7 respectively. After 8 years the ratio of the age of A to the age of B is 5 : 7. Find present age of C.

Answer:

• The present age of C is 56 years.

Step-by-step explanation:

Given that:

• The ratio of the present age of A, B and C is 4 : 6 : 7 respectively.
• After 8 years, ratio of the age of A to the age of B will be 5 : 7.

To Find:

• The present age of C.

Let us assume:

• A's present age be 4x.
• B's present age be 6x.
• C's present age be 7x.

After 8 years:

• A's age will be (4x + 8).
• B's age will be (6x + 8).
• C's age will be (7x + 8).

According to the question:

$\sf{\longmapsto\dfrac{4x+8}{6x+8}=\dfrac{5}{7}}$

After cross-multiplication,

$\sf{\longmapsto7(4x+8)=5(6x+8)}$

Opening the brackets,

$\sf{\longmapsto28x+56=30x+40}$

Transposing variables to LHS, constants to RHS and changing their sign,

$\sf{\longmapsto28x-30x=40-56}$

Subtracting,

$\sf{\longmapsto-2x=-16}$

$\sf{\longmapsto\;\not\!{-}2x=\;\not\!{-}16}$

$\sf{\longmapsto2x=16}$

Transposing 2 from LHS to RHS and changing its sign,

$\sf{\longmapsto x=\dfrac{16}{2}}$

Dividing the numbers,

$\sf{\longmapsto x=8}$

Hence,

• x = 8

Therefore,

• C's present age = 7x = 7 × 8 = 56 years

Hence, the present age of C is 56 years.