Question

5 years ago, sister’s age was 5 times the age of her brother and the sum of present ages of sister and brother is 34 years. what will be the age of her brother after 6 years?

Answer 1

$<b>Heya mate. ^_^. Solution below.$
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$<u>Your Question -</u>$

5 years ago, sister's age was 5 times the age of her brother and the sum of present ages is sister and brother is 34 years. What will be the age of her brother after 6 years.

$<u>Solution</u>$

Let the present age of brother be 'x'

Then, 5 years ago,
Brother's age = x - 5
Sister's age = 5(x-5) = 5x - 25

Present ages,
Brother's age = x
Sister's age = (5x-25)+5 = 5x - 20

But sum of present ages = 34.

=> x + (5x-20) = 34
=> x + 5x = 34 + 20
=> 6x = 54
=> x = 54/6
=> x = 9

Hence, brother's present age = x = 9
Sister's present age
= 5x - 20
= 5 × 9 - 20
= 45 - 20
= 25

Then, brother's age after 6 years
= 9 + 6
= 15 years.

And, sister's age after 6 years
= 25 + 6
= 31 years.

Lastly, your answer, i.e., age of brother 6 years = 15 years.
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Thank you. ;-)