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Each question given consists of question and two statements numbered I and II given you have to decide whether dat provided in statemnt sufficient to answer question read both statement and give answer
what is Rasika,s present age?
I.Rasika's age four years hence will be three times manisha's age that time
II.Rasika's age two years ago was five times manisha's age that time

A

if the data in statement I alone are sufficient to answer the question while the data in statement II alone are not sufficient to answer the question

B

if the data in statement II alone are sufficient to answer the question while the data in statement I alone are not sufficient to answer the question

C

if the data in statement I alone or in statement II alone are sufficient to answer the question

D

if the data in both statement I alone or in statement II alone are not sufficient to answer the question

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem of determining Rasika's present age based on the provided statements, we will analyze each statement step-by-step. ### Step 1: Analyze Statement I **Statement I:** Rasika's age four years hence will be three times Manisha's age that time. Let: - Rasika's present age = X - Manisha's present age = Y According to Statement I: - Rasika's age in 4 years = X + 4 - Manisha's age in 4 years = Y + 4 The equation derived from Statement I is: \[ X + 4 = 3(Y + 4) \] Expanding this gives: \[ X + 4 = 3Y + 12 \] \[ X - 3Y = 8 \] (Equation 1) ### Step 2: Analyze Statement II **Statement II:** Rasika's age two years ago was five times Manisha's age that time. According to Statement II: - Rasika's age two years ago = X - 2 - Manisha's age two years ago = Y - 2 The equation derived from Statement II is: \[ X - 2 = 5(Y - 2) \] Expanding this gives: \[ X - 2 = 5Y - 10 \] \[ X - 5Y = -8 \] (Equation 2) ### Step 3: Evaluate the Sufficiency of Each Statement Now we have two equations: 1. \( X - 3Y = 8 \) (from Statement I) 2. \( X - 5Y = -8 \) (from Statement II) We can solve these equations to find the values of X and Y. ### Step 4: Solve the Equations Subtract Equation 1 from Equation 2: \[ (X - 5Y) - (X - 3Y) = -8 - 8 \] This simplifies to: \[ -2Y = -16 \] \[ Y = 8 \] Now substituting \( Y = 8 \) back into Equation 1: \[ X - 3(8) = 8 \] \[ X - 24 = 8 \] \[ X = 32 \] ### Conclusion Rasika's present age is **32 years**. ### Final Answer The answer to the question "What is Rasika's present age?" is **32 years**.
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