Question

Present ages of anu and raj are in the ratio 4 : 5. Eight years from now the ratio of their ages will be 5:6. What is anu's present age?

Answer 1

Answer:

present age of anu = 4x years

present age of raj = 5x years

eight years from now anu age = 4x + 8 =5

= 4x = 8-5

=4x = 3

= x = 12years

present age of anu = 12 years

Answer 2

Given:-

• Present ages of Anu and Raj are in the ratio of 4:5.
• Eight years from now the ratio of their ages will be 5:6.

⠀

To find:-

• Anu's Present age?

⠀

Solution:-

★ Let the present ages of Anu and Raj be 4x years and 5x years respectively.

⠀

$\star{\boxed{\sf{\orange{After~ eight~ years~. Anu's~ age = (4x - 8)~ years;}}}}$

$\star{\boxed{\sf{\purple{Raj's~ eight~ years, Raj's~ age = (5x + 8)~ years.}}}}$

⠀

Therefore,

the ratio of their ages after 8 years

$\large{\tt{\longmapsto{\dfrac{4x + 8}{5x + 8}}}}$

This is given to be 5:6.

Therefore,

$\large{\tt{\longmapsto{\dfrac{4x + 8}{5x + 8} =\dfrac{5}{6}}}}$

⠀$\boxed{\sf{\red{Cross-multiplication~ gives}}}$

$\large{\tt{\longmapsto{6(4x + 8) = 5 (5x + 8)}}}$

$\large{\tt{\longmapsto{24x + 48 = 25x + 40}}}$

$\large{\tt{\longmapsto{24x + 48 - 40 = 25x}}}$

$\large{\tt{\longmapsto{24x + 8 = 25x}}}$

$\large{\tt{\longmapsto{8 = 25x - 24x}}}$

$\boxed{\large{\tt{\longmapsto{\green{8 = x}}}}}$

Therefore,

Anu's Present age:-

$\large{\tt{\longmapsto{4x = 4 × 8 = 32}}}$ years

Raj's Present age:-

$\large{\tt{\longmapsto{5x = 5 × 8 = 40}}}$ years

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