Raju is 19 years younger than Ram. After 5 years, their ages will be in the ratio of 2:3. Find their present ages.
Solution:
Let Raju's age be J and Ram's age be R. We can make two equations:
J + 19 = R (Raju is 19 years younger than Ram)
J + 5 R + 5 | = | 2 3 | (The ratio of (Raju's age in 5 years) to (Ram's age in five years) is 2/3.) |
We will cross-multiply the latter equation:
3(J + 5) = 2(R + 5)
At this point, one can either resolve the parenthesis, or substitute from the first equation R = J + 19 in R's place. It won't matter which you do. I'll substitute R = J + 19.
3(J + 5) = 2(J + 19 + 5) Now, add 19 + 5.
3(J + 5) = 2(J + 24) Then use distributive property.
3J + 15 = 2J + 48
J = 33.
Then check: If Raju is now 33 and Ram is 52, then in five years they will be 38 and 57. And, 38/57 = 2/3. So yes, it checks.
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