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Five years ago, Ram was three times as old as Shyam. Four years from now, Ram will be only twice as old as Shyam. What is the present age of Ram?
- a)30 years
- b)32 years
- c)36 years
- d)40 years
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Five years ago, Ram was three times as old as Shyam. Four years from n...
Shortcut:
Let Ram’s age be ‘x’
His age five years ago = 3 × (Shyam’s age five years ago)
∴ (x – 5) should be a multiple of 3
Only option that satisfies this condition is x = 32
Let Ram’s age be ‘x’
His age five years ago = 3 × (Shyam’s age five years ago)
∴ (x – 5) should be a multiple of 3
Only option that satisfies this condition is x = 32
Detailed solution:
Let the age of Ram’s and Shyam’s 5 years ago from present be x and y respectively
Then, Ram’s age was thrice as Shyam’s
⇒ x = 3y
Let the age of Ram’s and Shyam’s 5 years ago from present be x and y respectively
Then, Ram’s age was thrice as Shyam’s
⇒ x = 3y
Four years after from present, their age will x + 9 and y + 9
Now Ram’s age is twice the Shyam’s age
⇒ x + 9 = 2 × (y + 9)
⇒ 3y + 9 = 2y + 18 [∵ x = 3y]
∴ y = 9 and x = 3 × 9 = 27
∴ Ram’s present age = 27 + 5 = 32 years
⇒ x + 9 = 2 × (y + 9)
⇒ 3y + 9 = 2y + 18 [∵ x = 3y]
∴ y = 9 and x = 3 × 9 = 27
∴ Ram’s present age = 27 + 5 = 32 years
Most Upvoted Answer
Five years ago, Ram was three times as old as Shyam. Four years from n...
Problem:
Five years ago, Ram was three times as old as Shyam. Four years from now, Ram will be only twice as old as Shyam. What is the present age of Ram?
Solution:
Let's assume the present age of Ram to be R years and the present age of Shyam to be S years.
Step 1: Constructing equations based on given information
According to the problem statement, five years ago, Ram was three times as old as Shyam. We can write this as an equation:
R - 5 = 3(S - 5) ...(Equation 1)
Similarly, four years from now, Ram will be twice as old as Shyam. We can write this as another equation:
R + 4 = 2(S + 4) ...(Equation 2)
Step 2: Solving the equations
We have two equations with two unknowns (R and S). We can solve these equations to find the values of R and S.
Solving Equation 1:
Expanding the equation, we get:
R - 5 = 3S - 15
Simplifying the equation, we get:
R = 3S - 10 ...(Equation 3)
Solving Equation 2:
Expanding the equation, we get:
R + 4 = 2S + 8
Simplifying the equation, we get:
R = 2S + 4 ...(Equation 4)
Step 3: Equating the values of R from Equations 3 and 4
Since both equations are equal to R, we can equate them:
3S - 10 = 2S + 4
Simplifying the equation, we get:
S = 14
Step 4: Finding the value of R
Substituting the value of S in Equation 3, we can find the value of R:
R = 3(14) - 10
R = 42 - 10
R = 32
Therefore, the present age of Ram is 32 years.
Hence, the correct answer is option B) 32 years.
Five years ago, Ram was three times as old as Shyam. Four years from now, Ram will be only twice as old as Shyam. What is the present age of Ram?
Solution:
Let's assume the present age of Ram to be R years and the present age of Shyam to be S years.
Step 1: Constructing equations based on given information
According to the problem statement, five years ago, Ram was three times as old as Shyam. We can write this as an equation:
R - 5 = 3(S - 5) ...(Equation 1)
Similarly, four years from now, Ram will be twice as old as Shyam. We can write this as another equation:
R + 4 = 2(S + 4) ...(Equation 2)
Step 2: Solving the equations
We have two equations with two unknowns (R and S). We can solve these equations to find the values of R and S.
Solving Equation 1:
Expanding the equation, we get:
R - 5 = 3S - 15
Simplifying the equation, we get:
R = 3S - 10 ...(Equation 3)
Solving Equation 2:
Expanding the equation, we get:
R + 4 = 2S + 8
Simplifying the equation, we get:
R = 2S + 4 ...(Equation 4)
Step 3: Equating the values of R from Equations 3 and 4
Since both equations are equal to R, we can equate them:
3S - 10 = 2S + 4
Simplifying the equation, we get:
S = 14
Step 4: Finding the value of R
Substituting the value of S in Equation 3, we can find the value of R:
R = 3(14) - 10
R = 42 - 10
R = 32
Therefore, the present age of Ram is 32 years.
Hence, the correct answer is option B) 32 years.
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Five years ago, Ram was three times as old as Shyam. Four years from now, Ram will be only twice as old as Shyam. What is the present age of Ram?a)30 yearsb)32 yearsc)36 yearsd)40 yearsCorrect answer is option 'B'. Can you explain this answer?
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