the difference between the age of two brothers is 10 years,and 15 years ago their ages in ratio 2:1.assuming the age of younger brother x ,obtain an equation.also the ratio of their age 15 years hence.
Answers
Answer:
Their ages 15 years ago are, (x - 15) and (x - 25) respectively. Also, given 15 years ago their were in the ratio 2 : 1. ⇒ x = 50 - 15 = 35 years.
Given:
✰ The difference between the age of two brothers is 10 years.
✰ 15 years ago their ages in ratio 2:1.
To find:
✠ Assuming the age of younger brother x, obtain an equation.
✠ The ratio of their age 15 years hence.
Solution:
Let the age of younger brother be x years.
Then the age of elder brother = ( x + 10 ) years
15 years ago,
⤳ Age of younger brother = x - 15
⤳ Age of elder brother = x + 10 - 15
⤳ Age of elder brother = x - 5
We are provided that 15 years ago their ages in ratio 2:1. Like this we will get an equation and after that doing the required calculations we will find their present ages.
According to the question,
➛ ( x - 5 )/( x - 15 ) = 2/1
➛ x - 5 = 2( x - 15 )
➛ x - 5 = 2x - 30
➛ 2x - x = - 5 + 30
➛ x = 25
⤳ Age of elder brother = x + 10
⤳ Age of elder brother = 25 - 10
⤳ Age of elder brother = 35 years
∴ Their present ages are 25 years and 35 years respectively.
15 years hence,
⤳Respective ages are 35 + 15 = 50 and 25 + 15 = 40
Now, the ratio of their age 15 years hence,
➤ 50/40
➤ 5/4
∴ The ratio of their age 15 years hence = 5:4
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