Question 1

P can do a piece of work in 5 less days than Q. If both of them can do the same work in 1119 days, in how many days will Q alone do the same work ?

Accepted Answer

Let Q complete that work in 'L' days => 1 L + 1 L - 5 = 9 100 => 9 L 2 - 245 L + 500 = 0 L = 25 days.

Question 2

X can complete the work in 10 days, Y can do the same in 15 days. If they are hired for 5 days to do the work together, what is the work that left unfinished?

Accepted Answer

Given X can do in 10 days => 1 day work of X = 1/10 Y can do in 15 days => 1 day work of Y = 1/15 1day work of (X + Y) = 1/10 + 1/15 = 1/6 Given they are hired for 5 days => 5 days work of (X + Y) = 5 x 1/6 = 5/6 Therefore, Unfinished work = 1 - 5/6 = 1/6

Question 3

Three men, four women and six children can complete a work in 9 days. A women 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 9 days?

Accepted Answer

Given (3 Men + 4 Women + 6 Children) -----> 9 days But W = 2M and C = M/2 Now, convert Men and Children into Women by 3 W 2 + 4 W + 6 W 4 = > 3 2 + 4 + 3 2 = 7 Women Therefore, 7 women alone can complete this work in 9 days.

Question 4

A can complete 9/10 part of a work in 31 days. After that, with the help of B he can complete the remaining work in 4 days. In how many days will A and B together can complete that work ?

Accepted Answer

Remaining work = 1 - 9/10 = 1/10 => A & B together completes 1/10 of work in 4 days => 1 work can completed in ------ ? days Let it be x days => 4 1 10 = x 1 => x = 40 days. Hence, A & B together can complete the work in 40 days.

Question 5

Twenty men can do a work in eighteen days. Eighteen women can complete the same work in fifteen days. What is the ratio between the capacity of a woman and a man ?

Accepted Answer

(20 x 18) men can complete the work in in one day. one man's one day work = 1/360 (18 x 15) women can complete the work in 1 day 1 woman's one day work = 1/270 So, required ratio = 1 270 : 1 360 = 4:3

Question 6

16 men and 12 women can complete a work in 20 days. 18 women can complete the same work in 40 days. In how many days will 12 men 27 women complete the same work?

Accepted Answer

(16M + 12W) x 20 = 18W x 40 => 2M = 3W Then, Convert all men into women 12M + 27W = 27 + 12 x 3/2W = 45W Let number of days required be 'D' => 18 x 40 = 45 x D => D = 16 days.

Question 7

A tank has an inlet and outlet pipe. The inlet pipe fills the tank completely in 2 hours when the outlet pipe is plugged. The outlet pipe empties the tank completely in 6 hours when the inlet pipe is pluggeed. If there is a lekage also which is capa…

Accepted Answer

Rate of leakage = 8.33% per hour Net efficiency = 50 - (16.66 + 8.33)= 25% Time required = 100/25 = 4 hours

Question 8

28 Men and 52 women working together completes a work in 22.5 days. 35 men and 65 women working together on same work will complete it in how many days?

Accepted Answer

Clearly total persons are increased in 28/35 :: 52/65 = 4:5. As time is inversely proportional to men, so total time will decrease in the ratio 5:4. Hence, 22.5 x 4/5 = 18 days.

Question 9

In a hostel, there was food for 1000 students for one month. After 10 days, 1000 more students joined the hostel. How long would the students be able to carry on with the remaining food?

Accepted Answer

After 10 days, the remaining food would be sufficient for the 1000 students for 20 more days -->If 1000 more students are added, it shall be sufficient for only 10 days (as the no. of students is doubled, the days are halved).

Question 10

50 men can build a tank in 40days, but though they begin the work together, 5 men quit every ten days. The time needed to build the tank is ?

Accepted Answer

50 men can build a tank in 40 days Assume 1 man does 1 unit of work in 1 day Then the total work is 50×40 = 2000 units 50 men work in the first 10 days and completes 50×10 = 500 units of work 45 men work in the next 10 days and completes 45×10 = 450 units of work 40 men work in the next 10 days and completes 40×10 = 400 units of work 35 men work in the next 10 days and completes 35×10 = 350 units of work So far 500 + 450 + 400 + 350 = 1700 units of work is completed and Remaining work is 2000 - 1700 = 300 units 30 men work in the next 10 days. In each day, they does 30 units of work. Therefore, additional days required = 300/30 =10 Thus, total 10+10+10+10+10 = 50 days required.

Question 11

Adam and Smith are working on a project. Adam takes 6 hrs to type 36 pages on a computer, while Smith takes 5 hrs to type 40 pages. How much time will they take, working together on two different computers to type a project of 120 pages?

Accepted Answer

Number of pages typed by Adam in 1 hour = 36/6 = 6 Number of pages typed by Smith in 1 hour = 40/5 = 8 Number of pages typed by both in 1 hour = (6 + 8) = 14 Time taken by both to type 110 pages = (120 * 1/14) = 8 4 7 = 8 hrs 34 min.

Question 12

6 boys and 8 girls can do job in 10 days , 26 boys & 48 women do work in 2 days. Find time taken by 15 boys and 20 girls to do same work ?

Accepted Answer

One day work of 6 boys and 8 girls is given as 6b + 8g = 1/10 -------->(I) One day work of 26 boys and 48 women is given as 26b + 48w = 1/2 -------->(II) Divide both sides by 2 in (I) and then multiply both sides by 5 Now we get, 15b + 20g = 1/4. Therefore, 15 boys and 20 girls can do the same work in 4 days.

Question 13

After working for 8 days, Hari Ram finds that only 1/3 rd of the work has been done. He employs Satya who is 60% as efficient as Hari Ram. How many days more would Satya take to complete the work ?

Accepted Answer

1/3 ---- 8 1 -------? Hari can do total work in = 24 days As satya is 60% efficient as Hari, then Satya = 1/24 x 60/100 = 1/40 => Satya can do total work in 40 days 1 ----- 40 2/3 ---- ? => 26 2/3 days.

Question 14

Pavan and Sravan are two persons. If Pavan works with his actual efficiency and Sravan twice of his actual efficiency then it takes 25 days to complete the work. But If Pavan works twice of his actual efficiency and Sravan with his normal efficiency…

Accepted Answer

Let the Efficiency of pavan be E(P) Let the Efficiency of sravan be E(S) Here Work W = LCM(25,20) = 100 Now, E(P+2S) = 100/25 = 4 ....(1) E(2P+S) = 100/20 = 5 ....(2) Hence, from (1) & (2) we get E(S) = 1 => Number of days Savan alone work to complete the work = 100/1 = 100 days.

Question 15

Priya can do a work in 16 days. In how many days will the work be completed by Sai, if the efficiency of Sai is 60% more than that of Priya ?

Accepted Answer

Ratio of efficiencies of Priya and Sai is Sai : Priya = 160 : 100 = 8 : 5 Given Priya completes the work in 16 days Let number of days Sai completes the work be 'd' => 5×16 = 8×d d = 10 days. Therefore, number of days Sai completes the work is 10 days.

Question 16

Kaushalya can do a work in 20 days, while kaikeyi can do the same work in 25 days. They started the work jointly.Few days later Sumitra also joined them and thus all of them completed the whole work in 10 days. All of them were paid total Rs.700. Wh…

Accepted Answer

Efficiency of kaushalya = 5% Efficiency of kaikeyi = 4% Thus, in 10 days working together they will complete only 90% of the work. [(5+4)*10] =90 Hence, the remaining work will surely done by sumitra, which is 10%. Thus, sumitra will get 10% of Rs. 700, which is Rs.70

Question 17

Three taps P, Q and R can fill a tank in 12 hrs, 15 hrs and 20 hrs respectively. If P is open all the time and Q and R are open for one hour each alternately, starting with Q, then the tank will be full in how many hours ?

Accepted Answer

Given, P can fill in 12 hrs Q can fill in 15 hrs R can fill in 20 hrs => Volume of tank = LCM of 12, 15, 20 = 60 lit => P alone can fill the tank in 60/12 = 5 hrs => Q alone can fill the tank in 60/15 = 4 hrs => R alone can fill the tank in 60/20 = 3 hrs Tank can be filled in the way that (P+Q) + (P+R) + (P+Q) + (P+R) + .... => Tank filled in 2 hrs = (5+4) + (5+3) = 9 + 8 = 17 lit => In 6 hrs = 17 x 6/2 = 51 lit => In 7th hr = 51 + (5+4) = 51 + 9 = 60 lit => So, total tank will be filled in 7 hrs.

Question 18

P and Q can do a work in 4 hours and 12 hours respectively. P starts the work at 9am and they work alternately for one hour each. When will the work be completed ?

Accepted Answer

Work done by P and Q in the first two hours, working alternately = First hour P + Second hour Q ⇒ 1 4 + 1 12 = 1 3 work is completed in 2 hours Then, the total time required to complete the work by P and Q working alternately=2 x 3= 6hours Thus, work will be completed at 3pm.

Question 19

K can lay Highway road between two cities in 16 days. L can do the same job in 12 days. With the help of M, they completes the job in 4 days. How much days does it take for M alone to complete the work ?

Accepted Answer

Amount of work K can do in 1 day = 1/16 Amount of work L can do in 1 day = 1/12 Amount of work K, L and M can together do in 1 day = 1/4 Amount of work M can do in 1 day = 1/4 - (1/16 + 1/12) = 3/16 – 1/12 = 5/48 => Hence M can do the job on 48/5 days = 9 (3/5) days

Question 20

P, Q, and R can do a job in 12 days together. If their efficiency of working be in the ratio 3 : 8 : 5, Find in what time Q can complete the same work alone?

Accepted Answer

Given the ratio of efficiencies of P, Q & R are 3 : 8 : 5 Let the efficiencies of P, Q & R be 3x, 8x and 5x respectively They can do work for 12 days. => Total work = 12 x 16x = 192x Now, the required time taken by Q to complete the job alone = 162 x 8 x = 24 days.

Time and Work Questions