Question

1. Verma is three times as old as Sharma. 2 years ago he was five times as old as Sharma. What is the present age of Verma?
O A. 12 years
OB. 14 years
O C. 18 years
OD. 24 years

Answer 1

Answer:

option C) 12 years

Step-by-step explanation:

Given :

• Verma is three times as old as Sharma.
• 2 years ago he was five times as old as Sharma

To find :

the present age of Verma

Solution :

Let the present age of Verma be x years

and the present age of Sharma be y years

⇾ Verma is three times as old as Sharma

Hence, x = 3y

2 years ago,

Verma's age = (x - 2) years

Sharma's age = (y - 2) years

⇾ Verma was five times as old as Sharma.

 x - 2 = 5(y - 2)

x - 2 = 5y - 10

 5y - x = 10 - 2

 5y - x = 8

Substitute x = 3y,

 5y - 3y = 8

  2y = 8

   y = 8/2

   y = 4

Substitute y = 4 in x = 3y,

x = 3(4) = 12

Therefore,

the present age of Verma is 12 years

Answer 2

A n s w e r

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G i v e n

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• Verma is three times as old as Sharma

• 2 years ago he was five times as old as Sharma

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F i n d

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• Present age of Verma

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S o l u t i o n

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• Let the present age of Verma be "v"

• Let the present age of Sharme be "s"

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Given that , Verma is three times as old as Sharma

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Thus ,

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➜ v = 3s ⚊⚊⚊⚊ ⓵

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$\underline{\bold{\texttt{Verma's age 2 years ago :}}}$

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➜ v - 2 ⚊⚊⚊⚊ ⓶

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$\underline{\bold{\texttt{Sharma's age 2 years ago :}}}$

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➜ s - 2 ⚊⚊⚊⚊ ⓷

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Also given that , 2 years ago Verma was five times as old as Sharma

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From ⓶ & ⓷

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➜ v - 2 = 5(s - 2)

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➜ v - 2 = 5s - 10

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➜ 5s - v = -2 + 10

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➜ 5s - v = 8 ⚊⚊⚊⚊ ⓸

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⟮ Putting v = 3s from ⓵ to ⓸ ⟯

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➜ 5s - v = 8

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➜ 5s - 3s = 8

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➜ 2s = 8

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➜ $\sf s = \dfrac { 8 } { 2 }$

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➜ s = 4 ⚊⚊⚊⚊ ⓹

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• Hence the present age of sharma is 4 years

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⟮ Putting s = 4 from ⓹ to ⓵ ⟯

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➜ v = 3s

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➜ v = 3(4)

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➨ v = 12

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• Hence present age of Verma is 12 years

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∴ Option A. 12 years is correct