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Five years ago, Ram was thrice as old as Mohan. Ten years later Ram shall be twice as old as Mohan. What is the present age of Ram and Mohan?
- a)50 years, 20 years
- b)56 years, 24 years
- c)50 years, 24 years
- d)56 years, 20 years
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Five years ago, Ram was thrice as old as Mohan. Ten years later Ram sh...
Problem: Five years ago, Ram was thrice as old as Mohan. Ten years later Ram shall be twice as old as Mohan. What is the present age of Ram and Mohan?
Solution:
Let the present age of Ram and Mohan be R and M years respectively.
Five years ago,
Ram's age = R - 5,
Mohan's age = M - 5.
According to the problem,
(R - 5) = 3(M - 5) ...(1) [Five years ago, Ram was thrice as old as Mohan]
R + 10 = 2(M + 10) ...(2) [Ten years later Ram shall be twice as old as Mohan]
Solving equations (1) and (2), we get
R - 3M = -10 ...(3)
R - 2M = 10 ...(4)
Subtracting equation (4) from equation (3), we get
(-3M) - (-2M) = -10 - 10
-M = -20
Therefore, M = 20.
Putting this value of M in equation (4), we get
R - 2(20) = 10
R = 50
Hence, the present age of Ram is 50 years and the present age of Mohan is 20 years.
Therefore, the correct answer is option (a) 50 years, 20 years.
Solution:
Let the present age of Ram and Mohan be R and M years respectively.
Five years ago,
Ram's age = R - 5,
Mohan's age = M - 5.
According to the problem,
(R - 5) = 3(M - 5) ...(1) [Five years ago, Ram was thrice as old as Mohan]
R + 10 = 2(M + 10) ...(2) [Ten years later Ram shall be twice as old as Mohan]
Solving equations (1) and (2), we get
R - 3M = -10 ...(3)
R - 2M = 10 ...(4)
Subtracting equation (4) from equation (3), we get
(-3M) - (-2M) = -10 - 10
-M = -20
Therefore, M = 20.
Putting this value of M in equation (4), we get
R - 2(20) = 10
R = 50
Hence, the present age of Ram is 50 years and the present age of Mohan is 20 years.
Therefore, the correct answer is option (a) 50 years, 20 years.
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Community Answer
Five years ago, Ram was thrice as old as Mohan. Ten years later Ram sh...
Let present age of Ram be x years and present age of Mohan be y years.
x - 5 = 3 (y - 5)
⇒ x - 3y = -10 ...(1)
and x + 10 = 2(y + 10)
x - 2y = 10 ...(2)
x - 3y = -10
x - 2y = 10
Subtracting (1) and (2)
-y = - 20 ⇒ y = 20
Now x = 10 + 2y = 10 + 2 × 20 = 50
x - 5 = 3 (y - 5)
⇒ x - 3y = -10 ...(1)
and x + 10 = 2(y + 10)
x - 2y = 10 ...(2)
x - 3y = -10
x - 2y = 10
Subtracting (1) and (2)
-y = - 20 ⇒ y = 20
Now x = 10 + 2y = 10 + 2 × 20 = 50
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Five years ago, Ram was thrice as old as Mohan. Ten years later Ram shall be twice as old as Mohan. What is the present age of Ram and Mohan?a)50 years, 20 yearsb)56 years, 24 yearsc)50 years, 24 yearsd)56 years, 20 yearsCorrect answer is option 'A'. Can you explain this answer?
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