Question

The age of leena and heena are in the ratio of 7:5 . Ten years hence, the ratio of their ages will be 9:7 . Find thier present afe

Answer 1

Answer :

• Present age of Leena = 7x = 7 × 5 = 35 years
• Present age of Heena = 5x = 5 × 5 = 25 years

Given :

• The age of leena and heena are in the ratio of 7 : 5. Ten years hence, the ratio of their ages will be 9 : 7.

To Find :

• Their present ages.

Solution :

Put x in ratio

Now, their present ages are

• Present age of Leena = 7x
• Present age of Heena = 5x

After 10 years

• Leena's age = 7x + 10
• Heena's age = 5x + 10

It is given that

• After 10 years, ratios of their ages will be 9 : 7

According to question :

→ 7x + 10/5x + 10 = 9/7

→ 7 (7x + 10) = 9 (5x + 10)

→ 49x + 70 = 45x + 90

→ 49x - 45x = 90 - 70

→ 4x = 20

→ x = 20/4

→ x = 5

Now

• Present age of Leena = 7x = 7 × 5 = 35 years
• Present age of Heena = 5x = 5 × 5 = 25 years

Hence, the present ages of Leena and Heena are 35 years and 25 years respectively.

Answer 2

Given

• The age of Leena and Heena are in the ratios of 7:5.
• 10 years hence, the ratio of their ages will be 9:7.

⠀

To find

• Their present age.

⠀

Solution

• Let the ratio of their ages be x.

⠀

Then,

• Present age of Leena = 7x
• Present age of Heena = 5x

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★ After 10 years,

• Age of Leena will be = (7x + 10)
• Age of Heena will be = (5x + 10)

⠀

★ According to the question

$\large{\tt{\longmapsto{\dfrac{7x + 10}{5x + 10} = \dfrac{9}{7}}}}$

⠀

$\large{\tt{\longmapsto{7(7x + 10) = 9(5x + 10)}}}$

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$\large{\tt{\longmapsto{49x + 70 = 45x + 90}}}$

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$\large{\tt{\longmapsto{49x - 45x = 90 - 70}}}$

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$\large{\tt{\longmapsto{4x = 20}}}$

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$\large{\tt{\longmapsto{x = \cancel{\dfrac{20}{4}}}}}$

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$\large{\bf{\longmapsto{x = 5}}}$

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• Value of x is 5.

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★ By putting the values

$\tt\longrightarrow{Present\: age\: of\: Leena = 7(5) = 35\: years}$

$\tt\longrightarrow{Present\: age\: of\: Heena = 5(5) = 25\: years}$

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