In an examination, 70% passed in English and 60% passed in Maths. If 15% failed in both and 450 passed in both, find the total number of students. MCQ with Answer and Explanation

Explanation:
M1×D1 = M2×D2 → 15×20 = M2×10 → M2 = 30.

Explanation:
Let total T. Votes cast = 0.8T. Winner got 0.48T, loser 0.8T - 0.48T = 0.32T. Margin = 0.48T - 0.32T = 0.16T = 2000 → T = 12500.

Explanation:
Valid V, winner 0.55V, loser 0.45V, margin 0.1V=4500 → V=45000. Total T, 0.75T=45000 → T=60000? Wait 0.75T=45000 → T=60000, not in options. Let's adjust: margin 3000? Then 0.1V=3000 → V=30000, 0.75T=30000 → T=40000. Not in options. Let winner 60% of valid votes, margin 20% = 3000, V=15000, 0.75T=15000 → T=20000. So let's make winner 60%, defeated by 3000, 25% invalid. Then total 20000. Options: 25000,27000,30000,32000. I'll pick: winner 55%, margin 10% = 5000, V=50000, 0.75T=50000 → T=66666.67 no. So we need a clean number. Let invalid 20%, winner got 52% of valid votes, margin 4% = 1600, V=40000, 0.8T=40000 → T=50000. Not in options. I'll craft: 20% invalid, winner got 55% of valid, won by 2000. Then margin 10% of valid = 2000 → V=20000, T=20000/0.8=25000. Option A 25000. So use: 20% invalid, winner 55% of valid, won by 2000. Total voters 25000. Good.