
HCF = 44
LCM = 264
First number ÷ 2 = 44 ⟹ First number = 44 × 2 = 88
We are to find the second number.
✅ Step 1: Use the formula:
HCF×LCM=Product of the two numbers\text{HCF} \times \text{LCM} = \text{Product of the two numbers}
Substitute known values:
44×264=88×Second Number44 \times 264 = 88 \times \text{Second Number}
Calculate the left side:
44×264=11,61644 \times 264 = 11,616
Now solve:
Second Number=11,61688=132\text{Second Number} = \frac{11,616}{88} = 132
✅ Final Answer:
The other number is 132.
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We are given:
Total candidates = 2500
Failed in subject A = 35%
Failed in subject B = 42%
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:
Failed in A only
OR
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:
Failed only in A = Failed in A − Failed in both
Failed only in B = Failed in B − Failed in both
🔢 Step 2: Calculate numbers
Failed in A = 35% of 2500 = 0.35 × 2500 = 875
Failed in B = 42% of 2500 = 0.42 × 2500 = 1050
Failed in both = 15% of 2500 = 0.15 × 2500 = 375
Now:
Failed only in A = 875 − 375 = 500
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.