Question

The total of the present ages of A, B, C and D is 96 years. What is B's present age?
I. The average age of A, B and D is 20 years.
II. The average age of C and D is 25 years.

• A. A
• B. B
• C. C
• D. D
• A. A
• B. B
• C. C
• D. D
• A. A
• B. B
• C. C
• D. D
• A. A
• B. B
• C. C
• D. D

Answer 1

The Correct Option is D

Step 1: Understand the main question
We are told that the total of the present ages of A, B, C, and D is 96 years. The specific question is: What is B’s present age? We must check if Statement I alone, Statement II alone, both together, or neither give us sufficient data to find B’s exact age.

Step 2: Analyze Statement I
Statement I says: The average age of A, B, and D is 20 years.
This means: (A + B + D) ÷ 3 = 20
⇒ A + B + D = 60
Since the total of all four (A + B + C + D) = 96, we can substitute:
C = 96 – (A + B + D) = 96 – 60 = 36
So, from Statement I we get C’s age = 36, but we still do not know B’s age because A and D are unknown and their values can vary. Therefore, Statement I alone is not sufficient.

Step 3: Analyze Statement II
Statement II says: The average age of C and D is 25 years.
This means: (C + D) ÷ 2 = 25
⇒ C + D = 50
Now, since total (A + B + C + D) = 96, we can find A + B:
A + B = 96 – (C + D) = 96 – 50 = 46
But this still gives only the sum of A and B, not B alone. So Statement II alone is also not sufficient.

Step 4: Combine both statements I and II
From Statement I: A + B + D = 60
From Statement II: C + D = 50
And we already know A + B + C + D = 96.

Let’s try combining:
From total: A + B + C + D = 96
Substitute C + D = 50 → A + B + 50 = 96 → A + B = 46.
From Statement I: A + B + D = 60.
We already have A + B = 46, so D = 60 – 46 = 14.
If D = 14, then C + D = 50 ⇒ C = 36.
Now A + B = 46, but still A and B cannot be separated. Without another condition, B’s individual age remains unknown.

Step 5: Conclusion
Even when using both statements together, we can determine values of C and D, and the sum of A and B, but not the exact age of B individually. Therefore, the data given is still not sufficient to answer the question fully.

Final Answer: The correct option is (D): Both statements together are not sufficient.

Answer 2

Step 1: Understand the question
We are told that Deepak’s marks in Hindi are 15 more than the average of marks in four subjects (Hindi, Economics, Sociology, and Philosophy). The main question is: What are his marks in Philosophy? To answer, we need to check if Statement I alone, Statement II alone, or both together provide enough information.

Step 2: Translate the condition in the question
Let H = Hindi, E = Economics, S = Sociology, P = Philosophy.
According to the question:
H = [(H + E + S + P) ÷ 4] + 15

Multiply both sides by 4:
4H = H + E + S + P + 60
⇒ 3H = E + S + P + 60
This is one relation, but it still involves three unknowns (E, S, P) and one known expression of H.

Step 3: Analyze Statement I
Statement I: The total marks in Hindi and Philosophy = 12.
So H + P = 12.
This gives a relationship between H and P, but not an absolute value. Without more information, we cannot isolate P. Therefore, Statement I alone is not sufficient.

Step 4: Analyze Statement II
Statement II: The difference between Sociology and Economics = 120.
So |S – E| = 120.
This only relates S and E, but it gives nothing about P. Therefore, Statement II alone is not sufficient.

Step 5: Combine both statements
From the main relation: 3H = E + S + P + 60.
From Statement I: H + P = 12 ⇒ P = 12 – H.
Substitute into the main relation: 3H = E + S + (12 – H) + 60 ⇒ 3H = E + S + 72 – H ⇒ 4H = E + S + 72.
From Statement II: |S – E| = 120. This still leaves multiple possibilities for E and S, and consequently multiple possible values for H and P. Hence, even when combined, the data is not sufficient to find a unique value of P.

Step 6: Conclusion
Neither Statement I nor Statement II nor both together provide enough information to determine Deepak’s exact marks in Philosophy.

Final Answer: The correct option is (D): Data is not sufficient.

Answer 3

Step 1: Understand the question
We need to find the cost price (C.P.) of the suitcase purchased by Richard. Two statements are given, and we must check whether each one alone, or both together, are sufficient to answer this question.

Step 2: Analyze Statement I
Statement I: Richard got 20% concession on the labeled price.
If the labeled price is L, then Richard’s cost price = L – 20% of L = 0.8L.
This gives us a relation between C.P. and L, but without the value of L or any selling price, we cannot determine the actual C.P. Therefore, Statement I alone is not sufficient.

Step 3: Analyze Statement II
Statement II: Richard sold the suitcase for Rs 2000 with 25% profit on the labeled price.
Selling Price (S.P.) = 2000.
He sold it at 25% profit on the labeled price. That means:
S.P. = L + 25% of L = 1.25L.
So 1.25L = 2000 ⇒ L = 1600.
From this, we know the labeled price, but we cannot find the cost price unless we also know the concession. Therefore, Statement II alone is also not sufficient.

Step 4: Combine Statements I and II
From Statement II, we found L = 1600.
From Statement I, C.P. = 0.8L = 0.8 × 1600 = 1280.
Now we have the exact cost price.

Step 5: Conclusion
Both statements together are necessary to find the exact C.P. Individually, neither is sufficient.

Final Answer: The correct option is (C): Both statements together are necessary.

Answer 4

Step 1: Understand the question
We are told that B alone can complete a work in 12 days. We need to find in how many days A, B, and C together can complete the work. Two statements are given, and we need to check whether one alone or both together are sufficient to answer.

Step 2: Work rate of B alone
If B can complete the work in 12 days, then B’s 1-day work = 1/12 of the total work.

Step 3: Analyze Statement I
Statement I: A and B together can complete the work in 3 days.
So (A + B)’s 1-day work = 1/3.
Since B’s 1-day work = 1/12, A’s 1-day work = (1/3 – 1/12) = (4 – 1)/12 = 3/12 = 1/4.
Thus, A alone can complete the work in 4 days.
But with only this, we do not know C’s work rate, so we cannot determine the combined time of A + B + C. Therefore, Statement I alone is not sufficient.

Step 4: Analyze Statement II
Statement II: B and C together can complete the work in 6 days.
So (B + C)’s 1-day work = 1/6.
Since B’s 1-day work = 1/12, C’s 1-day work = (1/6 – 1/12) = (2 – 1)/12 = 1/12.
Thus, C alone can complete the work in 12 days.
But with only this, we do not know A’s rate, so we cannot determine A + B + C. Therefore, Statement II alone is also not sufficient.

Step 5: Combine Statements I and II
From Statement I, we found A’s 1-day work = 1/4.
From Statement II, we found C’s 1-day work = 1/12.
Now we know:
A’s 1-day work = 1/4, B’s 1-day work = 1/12, C’s 1-day work = 1/12.
So (A + B + C)’s 1-day work = 1/4 + 1/12 + 1/12 = 3/12 + 1/12 + 1/12 = 5/12.
Therefore, A + B + C can complete the work in 12/5 = 2.4 days = 2 days and 2/5 of a day.

Step 6: Conclusion
Both statements are necessary together. Individually, they are not sufficient.

Final Answer: The correct option is (C): Both statements together are necessary.