Question

The ages of Reena and Neema are in the ratio of 5:6.Five years from
now their ages will be in the ratio of 6:7.Find their present age.

Answer 1

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Answer 2

Answer:

• Reena's and Neema's present age is 25 and 30 years respectively.

Step-by-step explanation:

Given that:

• The present ages of Reena and Neema are in the ratio 5 : 6.
• Five years after, their ages will be in the ratio of 6 : 7.

To Find:

• Their present ages.

Let us assume:

• Present age of Reena and Neema be 5x and 6x respectively.

After 5 years:

• Reena's age = 5x + 5
• Neema's age = 6x + 5

According to the question:

$\sf{\longmapsto5x+5:6x+5=6:7}$

Writing the ratios in fraction,

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

By cross-multiplication:

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

Opening the brackets,

$\sf{\longmapsto35x+35=36x+30}$

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

$\sf{\longmapsto35x-36x=30-35}$

Subtracting,

$\sf{\longmapsto-x=-5}$

$\sf{\longmapsto\not\!{-}x=\not\!{-}5}$

$\sf{\longmapsto x=5}$

Hence,

• x = 5

Therefore,

• Reena's present age = 5x = 5 × 5 = 25 years
• Neema's present age = 6x = 6 × 5 = 30 years