1. Kim can do a work in 3 days while David can do the same work in 2 days. Both of them finish the work together and get Rs. 150. What is the share of Kim?

A. Rs. 30 B. Rs. 60 C. Rs. 70 D. Rs. 75

Answer: Option: B
Explanation: Kim's wages : David's wages = Kim's 1 day work : David's 1 day work = [latex]\frac{1}{3}[/latex] : [latex]\frac{1}{2}[/latex] = 2:3 Kim's share = [latex]\frac{2}{5}[/latex] * 150 = Rs. 60
2. A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?

A. Rs. 375 B. Rs. 400 C. Rs. 600 D. Rs. 800

Answer: Option: B
Explanation: C's 1 day's work = [latex]\frac{1}{3}[/latex] - ([latex]\frac{1}{6}[/latex] + [latex]\frac{1}{8}[/latex]) = [latex]\frac{1}{3}[/latex] - [latex]\frac{7}{24}[/latex] = [latex]\frac{1}{24}[/latex] A's wages : B's wages : C's wages [latex]\frac{1}{6}[/latex] : [latex]\frac{1}{8}[/latex]: [latex]\frac{1}{24}[/latex] = 4:3:1 C's share = [latex]\frac{1}{8}[/latex] * 3200 = Rs. 400
3. A and B together can complete a work in 12 days. A alone can complete it in 20 days. If B does the work only for half a day daily, then in how many days A and B together will complete the work?

A. 10 days B. 11 days C. 15 days D. 20 days

Answer: Option: C
Explanation: B's 1 day work = ([latex]\frac{1}{12}[/latex] - [latex]\frac{1}{20}[/latex]) = 1/30 Now, (A + B)'s 1 day work = ([latex]\frac{1}{20}[/latex] + [latex]\frac{1}{60}[/latex]) = [latex]\frac{1}{15}[/latex] So, A and B together will complete the work in 15 days
4. A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days A do the work if he is assisted by B and C on every third day?

A. 12 days B. 15 days C. 16 days D. 18 days

Answer: Option: B
Explanation: A's 2 day's work = ([latex]\frac{1}{20}[/latex] * 2) = [latex]\frac{1}{10}[/latex] (A + B + C)'s 1 day work = ([latex]\frac{1}{20}[/latex] + [latex]\frac{1}{30}[/latex] + [latex]\frac{1}{60}[/latex]) = [latex]\frac{1}{10}[/latex] Work done in 3 days = ([latex]\frac{1}{10}[/latex] + [latex]\frac{1}{10}[/latex]) = [latex]\frac{1}{5}[/latex] Now, [latex]\frac{1}{5}[/latex] work is done in 3 days. Whole work will be done in (3 * 5) = 15 days. 10 men = 12 women or 1 man = [latex]\frac{6}{5}[/latex] women Therefore 15 men + 6 women = (15 x [latex]\frac{6}{5}[/latex] + 6)women i.e,, 24 women Now 12 women can do the work in 10 days Therefore, 24 women can do it in = 5 days
5. 20 women can do a work in 9 days. After they have worked for 6 days. 6 more men join them. How many days will they take to complete the remaining work?

A. 3:4 B. 4:3 C. 5:3 D. Data inadequate

Answer: Option: B
Explanation: (20 * 16) women can complete the work in 1 day. 1 woman's 1 day work = [latex]\frac{1}{320}[/latex] (16 * 15) men can complete the work in 1 day 1 man's 1 day work = [latex]\frac{1}{240}[/latex] So, required ratio = [latex]\frac{1}{240}[/latex] : [latex]\frac{1}{320}[/latex]

1. 10 men and 15 women together can complete a work in 6 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work?

A. 90 B. 125 C. 145 D. 150

Answer: Option: A
Explanation: (A +B)’s 5 days work = 5 ([latex]\frac{1}{10}[/latex] +[latex]\frac{1}{20}[/latex]) = ¾ Remaining work =(1 -[latex]\frac{3}{4}[/latex]) = ¼ [latex]\frac{1}{20}[/latex]work is done by B in 1 day. Therefore, ¼ work is done by B in (20 x [latex]\frac{1}{4}[/latex])i.e.., 5 days
2. A and B can together finish a work in 30 days. They worked for it for 20 days and then B left. The remaining work was done by A alone in 20 more days. Alone can finish the work in?

A. 48 days B. 50 days C. 54 days D. 225 days

Answer: Option: D
Explanation: 1 man's 1 day work = 1/100 (10 men + 15 women)'s 1 day work = [latex]\frac{1}{6}[/latex] 15 women's 1 day work = ([latex]\frac{1}{6}[/latex] - [latex]\frac{10}{100}[/latex]) = [latex]\frac{1}{15}[/latex] 1 woman's 1 day work = [latex]\frac{1}{225}[/latex] 1 woman alone can complete the work in 225 days.
3. 12 men can complete a piece of work in 4 days, while 15 women can complete the same work in 4 days. 6 men start working on the job and after working for 2 days, all of them stopped working. How many women should be put on the job to complete the remaining work, if it so to be completed in 3 days?

A. 15 B. 18 C. 22 D. Data inadequate

Answer: Option: A
Explanation: 1 man's 1 day work = [latex]\frac{1}{48}[/latex]; 1 woman's 1 day work = 1/60. 6 men's 2 day's work = [latex]\frac{6}{48}[/latex] * 2 = [latex]\frac{1}{4}[/latex]. Remaining work = (1 - [latex]\frac{1}{4}[/latex]) = [latex]\frac{3}{4}[/latex] Now, [latex]\frac{1}{60}[/latex] work is done in 1 day by 1 woman. So, [latex]\frac{3}{4}[/latex] work will be done in 3 days by (60 * [latex]\frac{3}{4}[/latex] * [latex]\frac{1}{3}[/latex]) = 15 women
4. A man, a woman and a boy can complete a job in 3, 4 and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1/4 of a day?

A. 1 B. 4 C. 19 D. 41

Answer: Option: D
Explanation: (1 man + 1 woman)'s 1 day work = ([latex]\frac{1}{3}[/latex] + [latex]\frac{1}{4}[/latex]) = 7/12 Work done by 1 man and 1 woman in [latex]\frac{1}{4}[/latex] day = ([latex]\frac{7}{12}[/latex] * [latex]\frac{1}{4}[/latex]) = [latex]\frac{7}{48}[/latex] Remaining work = (1 - [latex]\frac{7}{48}[/latex]) = [latex]\frac{41}{48}[/latex] Work done by 1 boy in [latex]\frac{1}{4}[/latex] day = ( [latex]\frac{1}{12}[/latex] * [latex]\frac{1}{4}[/latex]) = [latex]\frac{1}{48}[/latex] Number of boys required = [latex]\frac{41}{48}[/latex] * 41 = 41.
5. 3 men, 4 women and 6 children can complete a work in 7 days. A woman does double the work a man does and a child does half the work a man does. How many women alone can complete this work in 7 days?

A. 7 B. 8 C. 12 D. Cannot be determined

Answer: Option: A
Explanation: Let 1 woman's 1 day work = x. Then, 1 man's 1 day work = [latex]\frac{X}{2}[/latex] and 1 child's 1 day work [latex]\frac{X}{4}[/latex]. So, ([latex]\frac{3X}{2}[/latex] + 4x + + [latex]\frac{6X}{4}[/latex]) = [latex]\frac{1}{7}[/latex] [latex]\frac{28X}{4}[/latex] = [latex]\frac{1}{7}[/latex] => x = [latex]\frac{1}{49}[/latex] 1 woman alone can complete the work in 49 days. So, to complete the work in 7 days, number of women required = [latex]\frac{49}{7}[/latex] = 7.

1. 12 men complete a work in 9 days. After they have worked for 6 days, 6 more men join them. How many days will they take to complete the remaining work?

A. 2 days B. 3 days C. 4 days D. 5 days

Answer: Option: A
Explanation: 1 man's 1 day work = [latex]\frac{1}{108}[/latex] 12 men's 6 day's work = [latex]\frac{1}{9}[/latex] * 6 = [latex]\frac{2}{3}[/latex] Remaining work = 1 - [latex]\frac{2}{3}[/latex] = [latex]\frac{1}{3}[/latex] 18 men's 1 day work = 1/108 * 18 = [latex]\frac{1}{6}[/latex] [latex]\frac{1}{6}[/latex] work is done by them in 1 day. [latex]\frac{1}{3}[/latex] work is done by them in 6 * [latex]\frac{1}{3}[/latex] = 2 days.
2. A take twice as much time as B or thrice as much time to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in?

A. 4 hours B. 6 hours C. 8 hours D. 12 hours

Answer: Option: B
Explanation: Suppose A, B and C take x, [latex]\frac{X}{2}[/latex] and [latex]\frac{X}{3}[/latex] respectively to finish the work. Then, ([latex]\frac{1}{X}[/latex] + [latex]\frac{2}{X}[/latex] + [latex]\frac{3}{X}[/latex]) = 1/2 [latex]\frac{6}{X}[/latex] = [latex]\frac{1}{2}[/latex] => x = 12 So, B takes 6 hours to finish the work.
3. 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?

A. 3 B. 5 C. 7 D. Cannot be determined

Answer: Option: C
Explanation: 1 women's 1 day work = [latex]\frac{1}{70}[/latex] 1 child's 1 day work = [latex]\frac{1}{140}[/latex] (5 women + 10 children)'s 1 day work = ([latex]\frac{5}{10}[/latex] + [latex]\frac{10}{40}[/latex]) = (1/14 + [latex]\frac{1}{14}[/latex]) = [latex]\frac{1}{7}[/latex] 5 women and 10 children will complete the work in 7 days.
4. If 12 men and 16 boys can do a piece of work in 5 days; 13 men and 24 boys can do it in 4 days, then the ratio of the daily work done by a man to that of a boy is?

A. 2:1 B. 3:1 C. 3:2 D. 5:4

Answer: Option: A
Explanation: Let 1 man's 1 day work = x and 1 boy's 1 day work = y. Then, 12x + 16y = [latex]\frac{1}{5}[/latex] and 13x + 24y = 1/4 Solving these two equations, we get: x = [latex]\frac{1}{100}[/latex] and y = [latex]\frac{1}{20}[/latex] Required ratio = x:y = [latex]\frac{1}{100}[/latex] : [latex]\frac{1}{200}[/latex] = 2:1
5. 4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?

A. 35 B. 40 C. 45 D. 50

Answer: Option: B
Explanation: Let 1 man's 1 day work = x and 1 woman's 1 day work = y. Then, 4x + 6y = [latex]\frac{1}{8}[/latex] and 3x + 7y = [latex]\frac{1}{10}[/latex] Solving these two equations, we get: x = [latex]\frac{11}{400}[/latex] and y = [latex]\frac{1}{400}[/latex] 1 woman's 1 day work = ([latex]\frac{1}{400}[/latex] * 10) = [latex]\frac{1}{40}[/latex]. Hence, 10 women will complete the work in 40 days