Percentage MCQs

Explanation:
1.15 × 0.85 = 0.9775. 0.9775x = 782 → x = 782/0.9775 = 800.

Explanation:
Milk = 24, water = 16. For milk:water = 1:2, water = 48, add 32 L.

Explanation:
(1.5N)/(0.75D) = 2N/D = 5/8 → N/D = 5/16.

Explanation:
CP=x, SP=1.2x. New CP=0.9x, new SP=1.2x+30 = 1.4×0.9x = 1.26x → 0.06x=30 → x=500.

Explanation:
Let total = T. Son 20%, left 80%. Daughter 30% of 80% = 24% of T, left 56%. Charity 10% of 56% = 5.6% of T, left 50.4% = 10080 → T = 10080/0.504 = 20000.

Explanation:
1.2 × 0.75 = 0.9. 0.9x = x - 36 → 0.1x = 36 → x = 360.

Explanation:
Valid votes V = 0.9T. Winner got 0.6V = 0.54T, loser 0.4V = 0.36T, margin 0.18T = 1800 → T = 10000.

Explanation:
Original x, xy=120. 0.8x(y+6)=120 → 96 + 4.8x = 120 → 4.8x = 24 → x=5, reduced = 0.8×5 = 4.

Explanation:
SI for 2 years = 1040-920 = 120, SI per year = 60. For 3 years, SI = 180, principal = 920-180 = 740.

Explanation:
Total distance = 200+300=500 m, time 25 sec, speed = 500/25 = 20 m/s = 20 × 18/5 = 72 kmph.

Explanation:
Let speed in still water = x, stream = y. 16/(x-y) + 24/(x+y) = 6; 12/(x-y) + 36/(x+y) = 6. Let 1/(x-y)=a, 1/(x+y)=b. 16a+24b=6, 12a+36b=6. Solving: a=1/4, b=1/12. So x-y=4, x+y=12 → x=8, y=4. Wait, x=8, not 10. I miscalculated: 16a+24b=6, divide by 2: 8a+12b=3. 12a+36b=6 → 2a+6b=1. From 2a+6b=1 → a=(1-6b)/2. Substitute: 8*(1-6b)/2 +12b = 4(1-6b)+12b = 4-24b+12b = 4-12b = 3 → b=1/12. Then a = (1-6/12)/2 = (1-0.5)/2 = 0.25 = 1/4. So x-y=4, x+y=12 → x=8. So answer 8 kmph. Option B 8 kmph. I'll correct options.

Explanation:
Let 1/(u-v)=a, 1/(u+v)=b. 16a+24b=6, 12a+36b=6. Solve: a=1/4, b=1/12 → u-v=4, u+v=12 → u=8.

Explanation:
2(A+B+C) = 1/12 + 1/15 + 1/20 = (5+4+3)/60 = 12/60 = 1/5 → A+B+C = 1/10. Together 10 days.

Explanation:
Ages 6x,7x. (6x+8)/(7x+8)=8/9 → 54x+72=56x+64 → 2x=8 → x=4. Sum=6x+7x=13x=52.

Explanation:
Rent 20%, left 80%. Food 25% of 80% = 20% of income, left 60%. Education 30% of 60% = 18% of income, left 42% = 8400 → income = 8400/0.42 = 20000? Wait, 8400/0.42 = 20000. So income 20000, option B. But I set D as 25000. Let's recalc: 42% = 8400 → income = 20000. So answer B. I'll correct options: A 18000, B 20000, C 22000, D 25000. So answer B.

Explanation:
0.9 × 1.2 = 1.08, 1.08x = 540 → x = 500.

Explanation:
Red=60, Blue=30, Green=10. Defective: Red 0.05×60=3, Blue 0.1×30=3, Green 0.2×10=2. Total defective=8%. So answer 8%.

Explanation:
CP=x, MP=1.5x, SP=1.5x×0.8=1.2x. Profit = 0.2x = 60 → x=300.

Explanation:
Vessel1: milk=2/5, water=3/5. Vessel2: milk=5/9, water=4/9. Desired milk=7/12. By alligation: (2/5) vs (5/9) to get 7/12. 2/5=0.4, 5/9≈0.5556, 7/12≈0.5833. Actually 0.5833 > 0.5556? No, 0.5833 > 0.5556, so 7/12 is greater than both? Wait 2/5=0.4, 5/9≈0.5556, 7/12≈0.5833. 0.5833 > 0.5556, so not possible by mixing because desired higher than both. I need ratios such that one is higher, one lower. Let Vessel1 milk=4/7, Vessel2 milk=2/3, desired=3/5=0.6. 4/7≈0.571, 2/3≈0.667. Alligation: (0.667-0.6):(0.6-0.571)=0.067:0.029 ≈ not neat. So I'll craft a clean one: Vessel1 milk:water = 2:1 (milk=2/3), Vessel2 = 1:2 (milk=1/3). Desired = 1:1 (milk=1/2). Alligation: (2/3-1/2):(1/2-1/3) = (1/6):(1/6)=1:1. So ratio 1:1. That's easy. For tough, a different mixture: Let Vessel1 3:2 (milk 3/5=0.6), Vessel2 2:3 (milk 0.4), desired 1:1 (0.5). Alligation: (0.6-0.5):(0.5-0.4)=0.1:0.1=1:1. Still easy. To make tough, I'll ask: How many litres from Vessel1 and Vessel2 to make 100 litres of 1:1. That's moderate. I'll put: Two alloys have copper 70% and 40%. In what ratio must they be mixed to get 50% copper? Alligation: (70-50):(50-40)=20:10=2:1. So first:second = 1:2? Actually, from 70% and 40% to 50%, the distance from 70 to 50 is 20, from 40 to 50 is 10, so ratio of second to first is 20:10 = 2:1. So ratio (first:second) = 1:2. That's okay. So I'll use: Two alloys contain 70% and 40% copper. In what ratio must they be mixed to get an alloy with 50% copper? Answer 1:2. That's a classic. I'll use it.

Explanation:
By alligation: (70-50):(50-40) = 20:10 = 2:1. The ratio of the alloys is inverse: 1:2.