Read each question, consider the options, then reveal the correct answer and explanation.
100 MCQs10 per page9 of 10
MCQ 81Pipes And Cisterns
A cistern is filled by two inlet pipes in 12 and 15 minutes, while an outlet can empty it in 6 minutes. The two inlets are opened for 5 minutes, then the outlet is also opened. How long after opening the outlet will the cistern become empty?
38 minutes
22 minutes
45 minutes
42 minutes
Correct answerC — 45 minutes
Explanation
The two inlets fill at 1/12+1/15=3/20 per minute. In 5 minutes they fill 3/4 of the cistern. With all three open, net rate=1/12+1/15−1/6=−1/60, so the cistern loses 1/60 per minute. Emptying 3/4 therefore takes 45 minutes.
MCQ 82Hcf And Lcm
Find the least positive integer that leaves remainder 4 when divided by 16, 18, and 20, but is exactly divisible by 7.
2256
865
2884
3332
Correct answerC — 2884
Explanation
A number leaving remainder 4 for 16,18,20 has the form 720k+4 because LCM(16,18,20)=720. We need 720k+4 to be divisible by 7. Since 720≡6 mod 7, 6k+4≡0 mod 7 gives k≡4 mod 7. The least positive k is 4, giving 720×4+4=2884.
MCQ 83Work And Time
A completes half of a work in 6 days, while B completes two-fifths of the same work in 10 days. How long will they take to complete the whole work together?
8 4/37 days
7 2/7 days
7 1/7 days
7 5/7 days
Correct answerA — 8 4/37 days
Explanation
A's full-work time is 12 days, so A's rate is 1/12. B's rate is (2/5)/10=1/25. Their combined rate is 1/12+1/25=37/300, so time=300/37=8 4/37 days. The printed source options do not contain this exact mathematical result.
MCQ 84Work And Wages
Shantanu can complete a work in 12 days and Manu can complete the same work in 10 days. If they work together, in what ratio should their wages be divided?
5:6
3:2
1:6
5:7
Correct answerA — 5:6
Explanation
For the same work period, wages are divided in proportion to work done, which is proportional to efficiency. Shantanu's efficiency is 1/12 work per day and Manu's is 1/10. Thus their wage ratio is (1/12):(1/10)=10:12=5:6.
MCQ 85Word Problems Based On Numbers
A fraction becomes 1/2 when 2 is added to its numerator and 1 to its denominator. It becomes 3/5 when 1 is added to its numerator and 2 is subtracted from its denominator. What is the original fraction?
3/5
2/7
1/7
2/5
Correct answerB — 2/7
Explanation
Let the fraction be n/d. From (n + 2)/(d + 1) = 1/2, we get d = 2n + 3. From (n + 1)/(d - 2) = 3/5, we get 5n + 5 = 3d - 6. Substituting d = 2n + 3 gives 5n + 5 = 6n + 3, so n = 2 and d = 7. The original fraction is 2/7.
MCQ 86Mixture Or Alligation
A container holds liquids A and B in the ratio 7:5. Nine litres of mixture are removed and replaced by B, making the ratio 7:9. How many litres of A were initially present?
21 litres
10 litres
20 litres
25 litres
Correct answerA — 21 litres
Explanation
Let initial quantities be 7x and 5x. Removing 9 litres removes 21/4 litres of A and 15/4 litres of B. After adding 9 litres of B, the ratio becomes (7x−21/4):(5x−15/4+9)=7:9. Solving gives x=3, so initial A=7x=21 litres.
MCQ 87Work And Time
A can complete a work in 18 days, while B can complete the same work in half the time taken by A. What fraction of the work can they complete together in one day?
1/6
1/8
1/9
2/7
Correct answerA — 1/6
Explanation
B takes 9 days because this is half of A's 18 days. Their one-day work rates are 1/18 and 1/9, so together they complete 1/18+1/9=3/18=1/6 of the work per day. In work problems, rates are added when people work together.
MCQ 88Word Problems Based On Numbers
The sum of two positive numbers is 2.5 times their difference. If their product is 84, what is their sum?
20
26
24
22
Correct answerA — 20
Explanation
Let S be the sum and D the positive difference. The condition gives S = 2.5D = 5D/2. Write S = 5k and D = 2k. For two numbers, xy = (S² - D²)/4. Thus 84 = (25k² - 4k²)/4 = 21k²/4, so k² = 16 and k = 4. Hence S = 5k = 20.
MCQ 89Work And Time
A factory has equal numbers of women and children. Normally women work 6 hours and children 4 hours daily. Workload rises by 50%, children may work at most 6 hours, and all workers are equally efficient. How many extra hours per day must each woman work?
5 hours
3 hours
4 hours
9 hours
Correct answerB — 3 hours
Explanation
If there are n women and n children, normal work is 6n+4n=10n worker-hours. A 50% increase requires 15n. Children can contribute at most 6n, so women must contribute 9n, or 9 hours each. Their extra time is 9−6=3 hours.
MCQ 90Speed, Time And Distance
Shantanu cycles along the boundary of a square field from corner A to the diagonally opposite corner C in 30 minutes at 16 km/h. What is the area of the square?
16 sq km
8 sq km
9 sq km
32 sq km
Correct answerA — 16 sq km
Explanation
Cycling along the boundary from A to opposite corner C covers two sides of the square. Distance in 30 minutes is 16×0.5=8 km, so 2s=8 and side s=4 km. Area=4²=16 sq km. The printed source options omit the correct value.
