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Roshan’s current age is 2 years less than 1.6 times that of Usha’s. 8 years ago, Usha’s age was 1 year more than half of Roshan’s age 8 years ago. What is Roshan’s present age in years?
- a)30
- b)39
- c)33
- d)42
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Roshan’s current age is 2 years less than 1.6 times that of Usha...
Let Roshan’s age be x and Usha’s age be y
Roshan’s current age is 2 years less than 1.6 times that of Usha’s,
⇒ x = 1.6y – 2
⇒ 8y – 5x = 10 ----(1)
8 years ago, Usha’s age was 1 year more than half of Roshan’s age 8 years ago,
⇒ 2y – x = 10
⇒ 8y – 4x = 40 ----(2)
From (1) and (2) we get,
⇒ 5x – 4x = 40 – 10
⇒ x = 30
∴ Roshan’s present age = 30 years
Most Upvoted Answer
Roshan’s current age is 2 years less than 1.6 times that of Usha...
Understanding the Problem
To find Roshan's present age, we need to set up the equations based on the information provided.
Defining Variables
- Let Usha's current age be \( U \).
- Roshan's current age is \( R \).
Setting Up Equations
1. From the first statement:
"Roshan’s current age is 2 years less than 1.6 times that of Usha’s."
This translates to:
\( R = 1.6U - 2 \)
2. From the second statement:
"8 years ago, Usha’s age was 1 year more than half of Roshan’s age 8 years ago."
Eight years ago, Usha's age was \( U - 8 \) and Roshan's age was \( R - 8 \).
This gives us the equation:
\( U - 8 = \frac{1}{2}(R - 8) + 1 \)
Simplifying, we get:
\( U - 8 = \frac{1}{2}R - 4 + 1 \)
\( U - 8 = \frac{1}{2}R - 3 \)
Rearranging leads to:
\( U = \frac{1}{2}R + 5 \)
Substituting and Solving
Now we have two equations:
1. \( R = 1.6U - 2 \)
2. \( U = \frac{1}{2}R + 5 \)
Substituting equation 2 into equation 1:
\( R = 1.6\left(\frac{1}{2}R + 5\right) - 2 \)
Expanding:
\( R = 0.8R + 8 - 2 \)
\( R - 0.8R = 6 \)
\( 0.2R = 6 \)
\( R = 30 \)
Conclusion
Thus, Roshan's present age is \( \textbf{30 years} \), corresponding to option 'A'.
To find Roshan's present age, we need to set up the equations based on the information provided.
Defining Variables
- Let Usha's current age be \( U \).
- Roshan's current age is \( R \).
Setting Up Equations
1. From the first statement:
"Roshan’s current age is 2 years less than 1.6 times that of Usha’s."
This translates to:
\( R = 1.6U - 2 \)
2. From the second statement:
"8 years ago, Usha’s age was 1 year more than half of Roshan’s age 8 years ago."
Eight years ago, Usha's age was \( U - 8 \) and Roshan's age was \( R - 8 \).
This gives us the equation:
\( U - 8 = \frac{1}{2}(R - 8) + 1 \)
Simplifying, we get:
\( U - 8 = \frac{1}{2}R - 4 + 1 \)
\( U - 8 = \frac{1}{2}R - 3 \)
Rearranging leads to:
\( U = \frac{1}{2}R + 5 \)
Substituting and Solving
Now we have two equations:
1. \( R = 1.6U - 2 \)
2. \( U = \frac{1}{2}R + 5 \)
Substituting equation 2 into equation 1:
\( R = 1.6\left(\frac{1}{2}R + 5\right) - 2 \)
Expanding:
\( R = 0.8R + 8 - 2 \)
\( R - 0.8R = 6 \)
\( 0.2R = 6 \)
\( R = 30 \)
Conclusion
Thus, Roshan's present age is \( \textbf{30 years} \), corresponding to option 'A'.
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Roshan’s current age is 2 years less than 1.6 times that of Usha’s. 8 years ago, Usha’s age was 1 year more than half of Roshan’s age 8 years ago. What is Roshan’s present age in years?a)30b)39c)33d)42Correct answer is option 'A'. Can you explain this answer?
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