
We are given:
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Total candidates = 2500
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Failed in subject A = 35%
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Failed in subject B = 42%
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Failed in both subjects = 15%
We are asked:
👉 How many candidates passed in either subject but not in both?
Let’s solve step-by-step with explanation and a Venn Diagram concept.
🧠 Step 1: Understand what is being asked
We are to find the number of students who failed in exactly one subject — that is:
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Failed in A only
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OR
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Failed in B only
This is equivalent to:
(Only A) + (Only B) = (Failed in A but not in B) + (Failed in B but not in A)
Use formula for set operations:
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Failed only in A = Failed in A − Failed in both
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Failed only in B = Failed in B − Failed in both
🔢 Step 2: Calculate numbers
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Failed in A = 35% of 2500 = 0.35 × 2500 = 875
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Failed in B = 42% of 2500 = 0.42 × 2500 = 1050
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Failed in both = 15% of 2500 = 0.15 × 2500 = 375
Now:
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Failed only in A = 875 − 375 = 500
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Failed only in B = 1050 − 375 = 675
So,
Passed in either subject but not in both = 500 + 675 = 1175
✅ Final Answer:
1175 candidates passed in either subject but not in both.
We are given:
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A invests some amount (let’s say ₹x) at the beginning
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B invests double the amount = ₹2x after 6 months
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C invests triple the amount = ₹3x after 8 months
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Total annual profit = ₹27,000
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We are to find C’s share in the profit
Let’s solve step-by-step using the concept of investment × time.
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🟢 Step 1: Calculate the effective capital contribution (investment × time)
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A: ₹x for 12 months ⇒ x × 12 = 12x
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B: ₹2x for 6 months ⇒ 2x × 6 = 12x
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C: ₹3x for 4 months (since 12 − 8 = 4 months) ⇒ 3x × 4 = 12x
So the ratio of their capital contributions is:
A : B : C = 12x : 12x : 12x = 1 : 1 : 1
That means profit is shared equally among A, B, and C.
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🟢 Step 2: Divide the total profit
Total profit = ₹27,000
Each partner gets 1/3rd:
C’s share=13×27000=₹9000\text{C’s share} = \frac{1}{3} × 27000 = ₹9000
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✅ Final Answer:
C’s share of the profit is ₹9,000.