Aptitudes SET2 51-100 Q&A

 

Q51. A sum of ₹20,000 amounts to ₹25,200 in 3 years at simple interest. Find the rate of interest.
Solution:
SI = 25,200 – 20,000 = 5,200.
SI = (P×R×T)/100 → 5,200 = (20,000×R×3)/100.
R = (5,200×100)/(60,000) = 8.67%.
Answer: 8.67% per annum.

 

Q52. A man covers 2/5 of a journey at 40 km/h and the rest at 60 km/h. Find his average speed.
Solution:
Let distance = 120 km (LCM of denominators).
Covered 48 km at 40 → time = 48/40 = 1.2 h.
Remaining 72 km at 60 → time = 72/60 = 1.2 h.
Total = 2.4 h, Distance = 120.
Avg speed = 120/2.4 = 50 km/h.
Answer: 50 km/h.

 

Q53. The cost price of 20 oranges is equal to the selling price of 16 oranges. Find gain %.
Solution:
Let CP per orange = 1 → CP(20) = 20.
SP(16) = 20 → SP per orange = 20/16 = 1.25.
Profit = 0.25 → % = (0.25/1)×100 = 25%.
Answer: 25% profit.

 

Q54. A pipe can fill a cistern in 10 hrs and another can empty it in 15 hrs. If both are opened together, find the time to fill the cistern.
Solution:
Fill = 1/10 per hr, Empty = –1/15.
Net = 1/10 – 1/15 = (3 – 2)/30 = 1/30.
Time = 30 hrs.
Answer: 30 hours.

 

Q55. A number is increased by 20% and then decreased by 20%. Find the net effect.
Solution:
Let number = 100. After +20% → 120. After –20% → 120×0.8 = 96.
Decrease = 4%.
Answer: 4% decrease.

 

Q56. A train of 240 m long crosses a pole in 24 seconds. Find its speed.
Solution:
Speed = Distance / Time = 240/24 = 10 m/s = 10×3.6 = 36 km/h.
Answer: 36 km/h.

 

Q57. A tank has 3 pipes A, B, C. A fills in 10 hrs, B in 12 hrs, C empties in 20 hrs. If all are opened, time to fill?
Solution:
A = 1/10, B = 1/12, C = –1/20.
LCM = 60 → (6+5–3)/60 = 8/60 = 2/15.
Time = 15/2 = 7.5 hrs.
Answer: 7.5 hours.

 

Q58. A sum becomes ₹2,420 in 2 years at compound interest at 10% p.a. Find principal.
Solution:
A = P(1+0.1)^2 = P×1.21.
2420 = 1.21P → P = 2000.
Answer: ₹2,000.

 

Q59. The average of 7 numbers is 35. If the average of first 6 numbers is 32, find the 7th number.
Solution:
Sum of 7 = 7×35 = 245.
Sum of 6 = 6×32 = 192.
7th = 245 – 192 = 53.
Answer: 53.

 

Q60. Ratio of speeds of A and B is 3:4. If A covers a distance in 40 minutes, B will cover it in?
Solution:
Time ∝ 1/speed.
Ratio of times = 4:3.
So B’s time = (3/4)×40 = 30 min.
Answer: 30 minutes.

 

Q61. A sum triples itself in 15 years at simple interest. Find the rate of interest.
Solution:
SI = 2P in 15 years.
Rate = (200/15)% = 13.33%.
Answer: 13.33% per annum.

 

Q62. A man spends 1/3 of his income on food, 1/4 on rent, and 1/5 on clothes. He saves the rest. If savings = ₹3,000, find income.
Solution:
Fraction spent = 1/3 + 1/4 + 1/5 = 20/60 + 15/60 + 12/60 = 47/60.
So savings = 13/60 of income.
Income = 3000×60/13 = 13,846.15.
Answer: ₹13,846 approx.

 

Q63. Find probability of getting sum 9 when two dice are thrown.
Solution:
Total = 36. Favorable pairs: (3,6),(4,5),(5,4),(6,3). = 4.
Probability = 4/36 = 1/9.
Answer: 1/9.

 

Q64. A card is drawn from pack. Find probability it is neither king nor queen.
Solution:
Kings = 4, Queens = 4 → total 8.
So favorable = 52–8 = 44.
Probability = 44/52 = 11/13.
Answer: 11/13.

 

Q65. A can do a work in 15 days, B in 25 days. In how many days will they finish together?
Solution:
Rate = 1/15 + 1/25 = (5+3)/75 = 8/75.
Time = 75/8 = 9.375 days.
Answer: 9.375 days (9 days 9 hrs).

 

Q66. A person borrows ₹5,000 at 12% per annum simple interest for 3 years. Find interest and total amount.
Solution:
SI = (5000×12×3)/100 = 1800.
Amount = 5000 + 1800 = 6800.
Answer: SI = ₹1,800, Amount = ₹6,800.

 

Q67. Average age of 40 students is 16. Teacher joins, new average 17. Find teacher’s age.
Solution:
Sum of 40 = 40×16 = 640.
Sum of 41 = 41×17 = 697.
Teacher = 697 – 640 = 57.
Answer: 57 years.

 

Q68. Speed of boat in still water 10 km/h, stream speed 2 km/h. Find time to travel 24 km downstream.
Solution:
Downstream speed = 10+2 = 12.
Time = 24/12 = 2 hrs.
Answer: 2 hours.

 

Q69. A cube has side 12 cm. Find its volume.
Solution:
Volume = a³ = 12³ = 1728 cm³.
Answer: 1,728 cm³.

 

Q70. A card is drawn from 52 cards. Find probability it is red or ace.
Solution:
Red cards = 26, Aces = 4. But 2 red aces counted twice.
So total = 26+4–2 = 28.
Probability = 28/52 = 7/13.
Answer: 7/13.

 

Q71. A sells a watch at 10% profit. If SP = ₹660, find CP.
Solution:
CP = SP/1.1 = 660/1.1 = 600.
Answer: ₹600.

 

Q72. A sum becomes ₹1,331 in 2 years at compound interest. If rate = 10% per annum, find principal.
Solution:
A = P(1.1)² = P×1.21.
1331 = 1.21P → P = 1100.
Answer: ₹1,100.

 

Q73. Average of first 50 odd numbers?
Solution:
Odd numbers = 1,3,5,…,99.
Average = (first + last)/2 = (1+99)/2 = 50.
Answer: 50.

 

Q74. The ratio of present ages of A and B is 5:7. After 6 years, ratio becomes 3:4. Find ages.
Solution:
Let ages = 5x, 7x.
(5x+6)/(7x+6) = 3/4 → cross multiply: 4(5x+6) = 3(7x+6).
20x+24 = 21x+18 → x=6.
A=30, B=42.
Answer: 30 & 42 years.

 

Q75. A train 150 m long crosses a man in 12 seconds. Find its speed in km/h.
Solution:
Speed = 150/12 = 12.5 m/s.
Convert = 12.5×3.6 = 45 km/h.
Answer: 45 km/h.

 

Q76. If CP = ₹800, profit = 15%, find SP.
Solution:
SP = 800×1.15 = 920.
Answer: ₹920.

 

Q77. A cricketer scores runs in 5 matches: 36, 48, 50, 42, 44. Find average.
Solution:
Sum = 220. Average = 220/5 = 44.
Answer: 44.

 

Q78. Probability of getting a king in single draw from pack of 52.
Solution:
Kings = 4. Probability = 4/52 = 1/13.
Answer: 1/13.

 

Q79. Two numbers are in ratio 3:4. If their LCM = 84, find numbers.
Solution:
Let 3x, 4x. LCM = 12x.
12x = 84 → x=7.
Numbers = 21, 28.
Answer: 21 and 28.

 

Q80. A man rows 20 km downstream in 2 hrs, same upstream in 4 hrs. Find speed of boat and stream.
Solution:
Downstream = 20/2=10. Upstream=20/4=5.
Boat = (10+5)/2 = 7.5. Stream = (10–5)/2=2.5.
Answer: Boat = 7.5 km/h, Stream = 2.5 km/h.

 

Q81. 12 men can complete work in 18 days. How many days for 9 men?
Solution:
Work = 12×18 = 216.
9 men → 216/9 = 24 days.
Answer: 24 days.

 

Q82. Find simple interest on ₹9,000 at 5% in 4 years.
Solution:
SI = (9000×5×4)/100 = 1800.
Answer: ₹1,800.

 

Q83. Average of 8 numbers is 14. If one no. is removed, average becomes 13. Find removed number.
Solution:
Sum of 8 = 112. Sum of 7 = 91. Removed = 21.
Answer: 21.

 

Q84. Two dice are rolled. Probability that product is even?
Solution:
Total=36. Odd product only if both odd: 3 odds each → 9 pairs.
So even = 36–9=27. Probability=27/36=3/4.
Answer: 3/4.

 

Q85. A box has 6 white, 4 black balls. Two drawn together. Probability both white?
Solution:
Total ways= C(10,2)=45. Favorable= C(6,2)=15.
P=15/45=1/3.
Answer: 1/3.

 

Q86. A’s income is 20% more than B’s. Find A:B.
Solution:
Let B=100, then A=120. Ratio = 120:100=6:5.
Answer: 6:5.

 

Q87. The sum of two numbers is 60, their difference is 16. Find numbers.
Solution:
x+y=60, x–y=16. Add →2x=76→x=38. Then y=22.
Answer: 38 & 22.

 

Q88. Find perimeter of circle with radius 7 cm.
Solution:
Circumference = 2πr = 2×3.14×7=43.96 cm.
Answer: ≈44 cm.

 

Q89. A can finish a work in 40 days, B in 50 days. Together in?
Solution:
Rate=1/40+1/50=(5+4)/200=9/200.
Time=200/9≈22.22 days.
Answer: ≈22.2 days.

 

Q90. If principal=₹5,000, amount=₹6,050 in 2 years at CI. Find rate.
Solution:
A=P(1+r)^2 →6050=5000(1+r)^2.
(1+r)^2=6050/5000=1.21 →1+r=1.1 →r=10%.
Answer: 10%.

 

Q91. A man walks 7 km at 4 km/h and 9 km at 6 km/h. Find avg speed.
Solution:
Time=7/4+9/6=1.75+1.5=3.25 hrs.
Total distance=16. Avg=16/3.25≈4.92 km/h.
Answer: ≈4.92 km/h.

 

Q92. 3 coins tossed. Probability of exactly 2 heads?
Solution:
Total=8. Favorable: HHT, HTH, THH=3.
P=3/8.
Answer: 3/8.

 

Q93. Find LCM of 18, 24, 30.
Solution:
18=2×3², 24=2³×3, 30=2×3×5.
LCM=2³×3²×5=360.
Answer: 360.

 

Q94. A shopkeeper sold an item at 15% loss. If SP=₹2550, find CP.
Solution:
CP=SP/(1–0.15)=2550/0.85=3000.
Answer: ₹3,000.

 

Q95. A man deposits ₹10,000 in bank at 12% CI compounded annually. Find amount after 2 years.
Solution:
A=10000(1.12)^2=10000×1.2544=12544.
Answer: ₹12,544.

 

Q96. The avg of 4 consecutive even numbers is 27. Find numbers.
Solution:
Let numbers= x, x+2, x+4, x+6.
Avg=(4x+12)/4 = x+3 = 27 → x=24.
Numbers=24,26,28,30.
Answer: 24,26,28,30.

 

Q97. A card drawn. Probability it is face card (J,Q,K).
Solution:
Face cards = 3×4=12.
P=12/52=3/13.
Answer: 3/13.

 

Q98. Find simple interest on ₹3,600 at 5% in 2.5 years.
Solution:
SI=(3600×5×2.5)/100=450.
Answer: ₹450.

 

Q99. A and B together can do work in 15 days, B alone in 25 days. How long will A alone take?
Solution:
Rate together=1/15, B=1/25.
A=1/15–1/25=(25–15)/375=10/375=2/75.
So time=75/2=37.5 days.
Answer: 37.5 days.

 

Q100. A man sells a book at 20% profit. If CP=₹150, find SP.
Solution:
SP=150×1.2=180.
Answer: ₹180.