Question

The difference between the ages of two brothers is 10 years. 15 years ago if the elder one was twice as older as the younger one. Find their present ages

Answer 1

given the difference between the ages of two brothers is 10 years.

let the age of elder brother be x yrs

therefore age of the younger brother = x - 10 yrs

ATQ, 15 yrs ago the elder brother was twice as older as the younger one.

➡ x - 15 = 2(x - 10 - 15)

➡ x - 15 = 2(x - 25)

➡ x - 15 = 2x - 50

➡ x - 2x = -50 + 15

➡ -x = -35

➡ x = 35 yrs

hence,

the present age of elder brother = x

= 35 yrs

and present age of younger brother = x - 10

= 35 - 10

= 25 yrs

Answer 2

• Let age of elder brother be M years.

» The difference between the ages of two brothers is 10 years.

• Means the age of younger brother is (M - 10) years

15 years ago ..

• Age of elder brother = (M - 15) years.

• Age of younger brother = (M - 10 - 15) = (M - 25) years.

» 15 years ago if the elder one was twice as older as the younger one.

A.T.Q.

=> M - 15 = 2(M - 25)

=> M - 15 = 2M - 50

=> M - 2M = - 50 + 15

=> - M = - 35

=> M = 35

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Age of elder brother = 35 years (M)

Age of younger brother = 25 years (M - 10)

_________ [ ANSWER ]

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✡ Verification :

The difference between the ages of two brothers is 10 years

From above calculations we have age of elder brother = 35 years

and

Age of younger brother = 25 years.

Difference of their ages = Age of elder brother - Age of younger brother

→ 35 - 25 = 10 years

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