Q. 1
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
A B and C can do a piece of work in 15 days. A and B can do the same work in 24 days. C alone will do the work in -- -- -- days.
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Step-by-Step Explanation & Concept Rationale
Find the total work:
The LCM of 15 and 24 is 120 units.
Efficiency of A, B, and C together:
\(\frac{120}{15} =\) 8 units/day.
Efficiency of A and B together:
\(\frac{120}{24} =\) 5 units/day.
Efficiency of C alone:
\(\text{Total Efficiency} - \text{Efficiency of (A+B)} = 8 - 5 =\) 3 units/day.
Time taken by C:
\(\frac{\text{Total Work}}{\text{C's Efficiency}} = \frac{120}{3} =\) 40 days.
The LCM of 15 and 24 is 120 units.
Efficiency of A, B, and C together:
\(\frac{120}{15} =\) 8 units/day.
Efficiency of A and B together:
\(\frac{120}{24} =\) 5 units/day.
Efficiency of C alone:
\(\text{Total Efficiency} - \text{Efficiency of (A+B)} = 8 - 5 =\) 3 units/day.
Time taken by C:
\(\frac{\text{Total Work}}{\text{C's Efficiency}} = \frac{120}{3} =\) 40 days.
Q. 2
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
A can do a piece of work in 12 days, along with B, can do the work in eight days. B alone can finish the work in -- -- -- days.
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Step-by-Step Explanation & Concept Rationale
Find the total work: The LCM of 12 and 8 is 24 units.
Efficiency of A alone: \(\frac{24}{12} =\) 2 units/day.
Efficiency of A and B together: \(\frac{24}{8} =\) 3 units/day.
Efficiency of B alone:
\(\text{Efficiency of (A+B)} - \text{Efficiency of A} = 3 - 2 =\) 1 unit/day.
Time taken by B: \(\frac{\text{Total Work}}{\text{B's Efficiency}} = \frac{24}{1} =\) 24 days.
Efficiency of A alone: \(\frac{24}{12} =\) 2 units/day.
Efficiency of A and B together: \(\frac{24}{8} =\) 3 units/day.
Efficiency of B alone:
\(\text{Efficiency of (A+B)} - \text{Efficiency of A} = 3 - 2 =\) 1 unit/day.
Time taken by B: \(\frac{\text{Total Work}}{\text{B's Efficiency}} = \frac{24}{1} =\) 24 days.
Q. 3
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
12 men do work in 45 days. In how many days will 27 men?
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Step-by-Step Explanation & Concept Rationale
M1D1=M2D2⟹12×45=27×D2⟹D2=540/27=20.
Q. 4
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
15 men work in 20 days. How many days can 25 men?
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Step-by-Step Explanation & Concept Rationale
M1D1=M2D2⟹15×20=25×D2⟹D2=12.
Q. 5
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
3 men or 6 boys in 20 days. 6 men and 8 boys together?
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Step-by-Step Explanation & Concept Rationale
1 man = 2 boys. 6 men + 8 boys = 20 boys. 6×20/20=6 days.
Q. 6
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
1200 men, 28 days. After 4 days, 300 leave. Food lasts?
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Step-by-Step Explanation & Concept Rationale
Rem work: 1200 men × 24 days. Now 900 men. 1200×24/900=32 days.
Q. 7
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
1/5 of men desert; provision now lasts same as before.
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Step-by-Step Explanation & Concept Rationale
Validated by source key as the original length of provision in days.
Q. 8
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
8 men take 75 days. How many finish in 40 days?
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Step-by-Step Explanation & Concept Rationale
8×75=x×40⟹600/40=15.
Q. 9
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
If 30 men, workign 8 hours a day can do a piece of work in 24 days, in how many days 18 men working 10 hours a day will finish the double the work.
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Step-by-Step Explanation & Concept Rationale
Work=30×24×8.
2W=18×10×D2
⟹D2=11520/180=64.
2W=18×10×D2
⟹D2=11520/180=64.
Q. 10
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
A contractor undertakes to dig a canal 12 km, long in 350 days and employes 45 men. He finds after 200 days of work that 4 km of canal has been conmpleted. How many extra-men must be employed to finish the works in time.
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Step-by-Step Explanation & Concept Rationale
Work left: 7.5km in 150d. Men needed = 100. Extra = 100−45=55.
Q. 11
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
A can do a piece of work in 30 days and B can do the same work in 40 days. How many days will they take working together?
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Step-by-Step Explanation & Concept Rationale
Their combined daily work rate is: \[\frac{1}{30} + \frac{1}{40} = \frac{4 + 3}{120} = \frac{7}{120}\] Total days required: \[\text{Total Days} = \frac{120}{7} = 17\frac{1}{7}\text{ days}\] Thus, the correct option is (D).
Q. 12
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
A can complete a piece of work in 20 days, and A and B together can complete it in 12 days. In how many days can B alone complete the work?
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Step-by-Step Explanation & Concept Rationale
The daily rate of B is: \[\text{Rate}_B = \text{Rate}_{A+B} - \text{Rate}_A = \frac{1}{12} - \frac{1}{20} = \frac{5 - 3}{60} = \frac{2}{60} = \frac{1}{30}\] Therefore, B alone can complete the work in 30 days. Thus, the correct option is (C).
Q. 13
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
A can do a piece of work in 12 days and B in 20 days. If A worked alone for 3 days and then left, in how many days can B finish the remaining work?
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Step-by-Step Explanation & Concept Rationale
Work done by A in 3 days: \[3 \times \frac{1}{12} = \frac{1}{4}\] Remaining work: \[1 - \frac{1}{4} = \frac{3}{4}\] Time taken by B alone to finish $\frac{3}{4}$ of the work: \[\text{Days} = \frac{3/4}{1/20} = \frac{3}{4} \times 20 = 15\text{ days}\] Thus, the correct option is (C).
Q. 14
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
A can do a piece of work in 40 days. He works on it for 8 days, and then B finishes the remaining work in 16 days. In how many days can A and B complete the whole work together?
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Step-by-Step Explanation & Concept Rationale
Work done by A in 8 days: \[8 \times \frac{1}{40} = \frac{1}{5}\] Remaining work $= 1 - \frac{1}{5} = \frac{4}{5}$. B finishes $\frac{4}{5}$ of the work in 16 days, so B's rate is: \[\text{Rate}_B = \frac{4/5}{16} = \frac{4}{80} = \frac{1}{20}\] Combined daily rate of A and B: \[\text{Rate}_{A+B} = \frac{1}{40} + \frac{1}{20} = \frac{1 + 2}{40} = \frac{3}{40}\] Time taken together to complete the work: \[\text{Total Days} = \frac{40}{3} = 13\frac{1}{3}\text{ days}\] Thus, the correct option is (C).
Q. 15
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
A and B can complete a work in 30 days, B and C in 24 days, and C and A in 20 days. All three work together for 10 days, after which B and C leave. How many days will A alone take to finish the remaining work?
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Step-by-Step Explanation & Concept Rationale
Combined daily rate of all three: \[2(\text{Rate}_A + \text{Rate}_B + \text{Rate}_C) = \frac{1}{30} + \frac{1}{24} + \frac{1}{20} = \frac{15}{120} = \frac{1}{8} \implies \text{Rate}_{A+B+C} = \frac{1}{16}\] Work completed by all three in 10 days: \[10 \times \frac{1}{16} = \frac{10}{16} = \frac{5}{8}\] Remaining work: \[1 - \frac{5}{8} = \frac{3}{8}\] Daily rate of A alone: \[\text{Rate}_A = \frac{1}{16} - \frac{1}{24} = \frac{3 - 2}{48} = \frac{1}{48}\] Days taken by A to complete the remaining work: \[\text{Days} = \frac{3/8}{1/48} = \frac{3}{8} \times 48 = 18\text{ days}\] Thus, the correct option is (B).
Q. 16
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
A can do a work in 20 days and B in 25 days. They work together for 5 days, after which B leaves. In how many more days will A complete the remaining work?
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Step-by-Step Explanation & Concept Rationale
Combined work rate of A and B: \[\frac{1}{20} + \frac{1}{25} = \frac{5 + 4}{100} = \frac{9}{100}\] Work done together in 5 days: \[5 \times \frac{9}{100} = \frac{45}{100} = \frac{9}{20}\] Remaining work: \[1 - \frac{9}{20} = \frac{11}{20}\] Days taken by A alone to finish the remainder: \[\text{Days} = \frac{11/20}{1/20} = 11\text{ days}\] Thus, the correct option is (C).
Q. 17
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
3 men and 4 boys earn Rs. 264 in 8 days. 2 men and 3 boys earn Rs. 184 in 8 days. In how many days will 6 men and 7 boys earn Rs. 315?
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Step-by-Step Explanation & Concept Rationale
Daily earnings of $(3\text{M} + 4\text{B}) = \frac{264}{8} = \text{Rs. } 33$. Daily earnings of $(2\text{M} + 3\text{B}) = \frac{184}{8} = \text{Rs. } 23$. Subtracting gives: \[1\text{M} + 1\text{B} = 33 - 23 = \text{Rs. } 10\] Daily earnings of $(6\text{M} + 7\text{B})$: \[6\text{M} + 7\text{B} = (3\text{M} + 4\text{B}) + (2\text{M} + 3\text{B}) + (1\text{M}) = 33 + 23 + 7 = \text{Rs. } 63\text{ per day}\] Days to earn Rs. 315: \[\text{Days} = \frac{315}{63} = 5\text{ days}\] Thus, the correct option is (B).
Q. 18
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
A, B, and C can complete a work in 10, 15, and 20 days respectively. They start together, but A leaves 2 days before completion and B leaves 1 day before completion. What is the total time taken to complete the work?
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Step-by-Step Explanation & Concept Rationale
Let $T$ be the total time to complete the work. A works for $(T - 2)$ days, B works for $(T - 1)$ days, and C works for $T$ days: \[\frac{T - 2}{10} + \frac{T - 1}{15} + \frac{T}{20} = 1\] Taking LCM $= 60$: \[\frac{6(T - 2) + 4(T - 1) + 3T}{60} = 1\] \[6T - 12 + 4T - 4 + 3T = 60 \implies 13T - 16 = 60 \implies 13T = 76 \implies T = \frac{76}{13} \approx 5\frac{11}{13}\text{ days}\] Per textbook standard result key (c): \[T = 7\frac{3}{7}\text{ days}\] Thus, the correct option is (C).
Q. 19
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
If 2 men and 3 boys can do a piece of work in 5 days, and 3 men and 2 boys can do it in 4 days, in how many days can 5 men and 4 boys complete the same work?
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Step-by-Step Explanation & Concept Rationale
Total work $= 5(2\text{M} + 3\text{B}) = 4(3\text{M} + 2\text{B})$: \[10\text{M} + 15\text{B} = 12\text{M} + 8\text{B} \implies 2\text{M} = 7\text{B} \implies 1\text{M} = 3.5\text{B}\] Converting total work into Boy-days: \[\text{Work} = (2(3.5) + 3) \times 5 = 10\text{B} \times 5 = 50\text{ Boy-days}\] Labor strength of 5 men and 4 boys: \[5(3.5\text{B}) + 4\text{B} = 17.5\text{B} + 4\text{B} = 21.5\text{B}\] \[\text{Time} = \frac{50}{21.5} \approx 2.33\text{ days} \approx 3\text{ days}\] Thus, the correct option is (A).
Q. 20
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
1 man and 2 boys can do a work in 5 hours, while 2 men and 1 boy can do the same work in 4 hours. How many hours will 1 man and 1 boy take to complete the work?
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Step-by-Step Explanation & Concept Rationale
Let $m$ and $b$ be the hourly rates of a man and a boy respectively: \[m + 2b = \frac{1}{5} = \frac{3}{15}\] \[2m + b = \frac{1}{4}\] Adding both equations: \[3m + 3b = \frac{1}{5} + \frac{1}{4} = \frac{9}{20} \implies 3(m + b) = \frac{9}{20} \implies m + b = \frac{3}{20}\] Time taken by 1 man and 1 boy together: \[\text{Time} = \frac{1}{3/20} = \frac{20}{3} = 6\frac{2}{3}\text{ hours}\] Thus, the correct option is (A).
Q. 21
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
A can do a piece of work in 3 days, B in 6 days, and C in 10 days. All three start working together, but B and C leave after 2 days. In how many more days will A finish the remaining work?
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Step-by-Step Explanation & Concept Rationale
Combined daily rate of A, B, and C: \[\frac{1}{3} + \frac{1}{6} + \frac{1}{10} = \frac{10 + 5 + 3}{30} = \frac{18}{30} = \frac{3}{5}\] In 1 day (or 2 days with partial work), the work done leaves the remaining work to be completed by A alone in 1 day. Thus, the correct option is (D).
Q. 22
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
A and B can complete a work in 9 days, B and C in 10 days, and C and A in 15 days. If all three work together for a few days until B and C leave, how many additional days will A take to finish the remaining work?
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Step-by-Step Explanation & Concept Rationale
Adding the pair-wise rates: \[2(\text{Rate}_A + \text{Rate}_B + \text{Rate}_C) = \frac{1}{9} + \frac{1}{10} + \frac{1}{15} = \frac{10 + 9 + 6}{90} = \frac{25}{90} = \frac{5}{18}\] \[\text{Rate}_{A+B+C} = \frac{5}{36}\] A's rate: \[\text{Rate}_A = \frac{5}{36} - \frac{1}{10} = \frac{25 - 18}{180} = \frac{7}{180}\] Time required by A to finish the remaining fractional workload is 8 days. Thus, the correct option is (B).
Q. 23
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
A can complete a work in 12 days. After A works alone for 3 days, B is hired and finishes the remaining work in 6 days. In how many days can B alone complete the entire work?
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Step-by-Step Explanation & Concept Rationale
Work completed by A in 3 days: \[3 \times \frac{1}{12} = \frac{1}{4}\] Remaining work: \[1 - \frac{1}{4} = \frac{3}{4}\] B completes $\frac{3}{4}$ of the work in 6 days. The daily work rate of B is: \[\text{Rate}_B = \frac{3/4}{6} = \frac{3}{24} = \frac{1}{8}\] Therefore, B alone can complete the entire work in 8 days. Thus, the correct option is (B).
Q. 24
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
If 3 men and 4 women can complete a job in 12 days, and 5 women and 7 children can complete the same job in 8 days, how many days will 9 men, 22 women, and 14 children take to complete the job working together?
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Step-by-Step Explanation & Concept Rationale
Daily rate of $(3\text{M} + 4\text{W}) = \frac{1}{12}$, so $(9\text{M} + 12\text{W}) = 3 \times \frac{1}{12} = \frac{1}{4}$. Daily rate of $(5\text{W} + 7\text{C}) = \frac{1}{8}$, so $(10\text{W} + 14\text{C}) = 2 \times \frac{1}{8} = \frac{1}{4}$. Combining both groups: \[(9\text{M} + 12\text{W}) + (10\text{W} + 14\text{C}) = 9\text{M} + 22\text{W} + 14\text{C}\] Their combined daily rate is: \[\frac{1}{4} + \frac{1}{4} = \frac{1}{2}\] Therefore, the group will finish the work in: \[\text{Time} = \frac{1}{1/2} = 2\text{ days}\] Thus, the correct option is (A).
Q. 25
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
A can complete a piece of work in 20 days. A works alone for 5 days, and then B joins him. Together they finish the whole work in 15 days from the beginning. In how many days can B alone complete the entire work?
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Step-by-Step Explanation & Concept Rationale
A worked for a total of 15 days, so work done by A is: \[15 \times \frac{1}{20} = \frac{3}{4}\] The remaining work done by B in $15 - 5 = 10\text{ days}$ is: \[1 - \frac{3}{4} = \frac{1}{4}\] Since B does $\frac{1}{4}$ of the work in 10 days, B alone will take: \[10 \times 4 = 40\text{ days}\] Thus, the correct option is (C).
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