Question

The ratio of 'a' and 'b' 3:1, after 15 years their ratio would be 2:1,
then what are their present ages?​

Answer 1

Answer:

Step-by-step explanation:

Given, ratio of age of A and B=3:1

Let the ages of A and B be 3x and x, respectively.

Now, 15 years hence,

age of A=3x+15 and age of B=x+15.

Then,

x+15

3x+15

​

=

1

2

​

⟹ 3x+15=2(x+15)

⟹ 3x+15=2x+30.

Transposing x terms to one side, we get,

⟹ 3x−2x=30−15

⟹x=15.

∴A's age =3×15=45 years

and B's age =x=15 years.

Answer 2

$\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}$

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$\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}$

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• The ratio of ages of 'a' and 'b' is 3:1

• After 15 years their ratio of ages would be 2:1

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$\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}$

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• Their present ages

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$\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}$

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Given that the ratio of ages of 'a' and 'b' is 3:1

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So,

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• Let the present age of a be '3z'

• Let the present age of b be '1z'

$\:\:$

$\underline{ \underline{\bold{\texttt{Present age of a :}}}}$

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➠ 3z ⚊⚊⚊⚊ ⓵

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$\underline{ \underline{\bold{\texttt{Present age of b :}}}}$

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➠ 1z ⚊⚊⚊⚊ ⓶

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$\underline{ \underline{\bold{\texttt{a's age after 15 years :}}}}$

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➠ 3z + 15

$\:\:$

$\underline{ \underline{\bold{\texttt{b's age after 15 years :}}}}$

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➠ 1z + 15

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Also given that , after 15 years their ratio of ages would be 2:1

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Thus ,

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: ➜ $\sf \dfrac { 3z + 15 } { z + 15 } = \dfrac { 2 } { 1 }$

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⟮ Cross multiplying ⟯

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: ➜ 1(3z + 15) = 2(z + 15)

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: ➜ 3z + 15 = 2z + 30

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: ➜ 3z - 2z = 30 - 15

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: ➜ z = 15 ⚊⚊⚊⚊ ⓷

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⟮ Putting z = 15 from ⓷ to ⓵ ⟯

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: ➜ 3z

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: ➜ 3(15)

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: : ➨ 45

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• Hence the present age of 'a' is 45 years

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⟮ Putting z = 15 from ⓷ to ⓶ ⟯

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: ➜ 1z

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: ➜ 1(15)

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: : ➨ 15

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• Hence the present age of 'b' is 15 years

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∴ The present ages of 'a' & 'b' are 45 years and 15 years respectively