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A mixture contains 30% alcohol. If 10 liters of pure alcohol is added to 50 liters of mixture, what is the new percentage of alcohol?
Explanation:
Initial alcohol = 50 × 0.3 = 15 liters. After adding 10 liters: total alcohol = 25 liters, total volume = 60 liters. Percentage = 25/60 × 100 ≈ 41.67% ≈ 40-45%. Recalculating for 50%: (15+10)/(50+10) = 25/60 = 41.67%. Closest is 40%. Check if answer is 50%: would require different quantities.
Two workers can complete a project: alone A takes 15 days, alone B takes 20 days. After A works for 5 days, B joins. How many more days are needed?
A
5 days
B
6 days
C
7 days
D
8 days
Correct Answer:
B. 6 days
Explanation:
A's work in 5 days = 5/15 = 1/3. Remaining = 2/3. Combined rate = 1/15 + 1/20 = 7/60. Time for remaining = (2/3)/(7/60) = (2/3) × (60/7) = 40/7 ≈ 5.7 ≈ 6 days.
A number is increased by 25% and then decreased by 20%. What is the net percentage change?
Explanation:
Let number = 100. After 25% increase: 125. After 20% decrease on 125: 125 × 0.8 = 100. Net change = 0%
If the ratio of boys to girls in a class is 3:2 and there are 45 boys, how many girls are there?
Explanation:
Boys:Girls = 3:2. If boys = 45, then 3x = 45, x = 15. Girls = 2x = 30
A shopkeeper buys an item for Rs. 400 and sells it at a profit of 35%. What is the selling price?
A
Rs. 525
B
Rs. 535
C
Rs. 540
D
Rs. 560
Correct Answer:
C. Rs. 540
Explanation:
SP = CP + Profit = 400 + (35% of 400) = 400 + 140 = Rs. 540
Two numbers are in the ratio 5:8. If their sum is 130, find the larger number.
Explanation:
Let numbers be 5x and 8x. 5x + 8x = 130, 13x = 130, x = 10. Larger number = 8 × 10 = 80
A trader marks an item 50% above cost price and gives 20% discount. What is the profit percentage?
Explanation:
Let CP = 100. MP = 150. SP = 150 × 0.8 = 120. Profit = 20%
A man can complete a work in 12 days. A woman can complete it in 15 days. If they work together, in how many days will they complete it?
A
6.5 days
B
6.67 days
C
7 days
D
7.5 days
Correct Answer:
B. 6.67 days
Explanation:
Work rate combined = 1/12 + 1/15 = 5/60 + 4/60 = 9/60 = 3/20. Time = 20/3 ≈ 6.67 days
A sum of Rs. 1200 becomes Rs. 1440 in 2 years at simple interest. What is the rate of interest?
Explanation:
SI = 1440 - 1200 = 240. Rate = (SI × 100)/(P × T) = (240 × 100)/(1200 × 2) = 10%
A train travels 450 km in 5 hours. What is its average speed?
A
80 km/h
B
85 km/h
C
90 km/h
D
95 km/h
Correct Answer:
C. 90 km/h
Explanation:
Speed = Distance/Time = 450/5 = 90 km/h
