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# x and y working together can complete a piece of work in 18 days

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### Mohammed

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## If A and B together can complete a piece of work in 15 days and B alone in 20 days. In how many days a alone can complete the work ?

Click here👆to get an answer to your question ✍️ If A and B together can complete a piece of work in 15 days and B alone in 20 days. In how many days a alone can complete the work ?

Question

A

B

C

D

## 45 days

Medium Open in App

Updated on : 2022-09-05

Solution Verified by Toppr

Correct option is B)

a and b can complete the work in 15 days.

Percentage of work done by a and b in one day = 100/15=6.66%

b alone can complete the whole work in 20 days.

So, percentage of work done by b in one day = 100/20=5%

Percentage of work done by a in one day = 6.66-5=1.66%

Thus, a can complete the whole work alone in = 100/1.66=60 days (approx)

Alternatively,

a and b can complete the work in = 15 days

Part of work done by a and b in one day= 1/15

b can complete the work alone in = 20 days.

so, part of work done by b in one day = 1/20

Part of work done by a = 1/15 - 1/20= 1/60

a can complete the work in = 1/(1/60) = 60 days.

19 8

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## X and Y together can complete a work in 20 days while Y and Z together can complete it in 24 days. After X worked on it for 10 days and Y for 18 days, Z alone completed the remaining work in 13 days. X and Z together can complete 75% of the work in?

Answer (1 of 12): Let x,y,z be the work done by X,Y,Z in one day. Divide the work into120 equal units. x+y=120/20=6..eq(1) y+z=120/24=5..eq(2) From eq(1)and eq(2) x-z=1..eq(3) 10x+18y+13z=120..eq(4) 10(x+y)+8(y+z)+5z=120 Using eq(1) and eq(2) in eq(4) 10(6)+8(5)+5z=120 5z=20 z=4..eq(5) ...

X and Y together can complete a work in 20 days while Y and Z together can complete it in 24 days. After X worked on it for 10 days and Y for 18 days, Z alone completed the remaining work in 13 days. X and Z together can complete 75% of the work in?

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x + y = 1/20 , y+z = 1/24. Hence

10x + 18y + 13z = 1

10 * 1/20 + 8 *1/24 + 5z = 1

5z = 1- 5/6 = 1/6, z = 1/30

So, y = 6/24*30 = 1/120 , x = 6/120 — 1/120 = 1/24

x+z = 1/24 + 1/30 = 54/24*30 = 3/40

So they do 75% work in 3/4* 40/3 = 10 days

Related questions

X, y and z take 18 days to complete a piece of work. If x works alone he finishes the work in 36 days and if y works alone he finishes it in 60 days. How long will it take z to complete the work alone?

X can complete a work in the same time in which Y and Z together can do it. If X and Y together can finish it in 10 days and Z alone in 15 days, then Y alone can do it in how many days?

In climbing a round pole of 80 metres height, a monkey climbs 5 metres in a minute and slips 2 metres in the alternate minute. How much time would the monkey take to get to the top of the pole?

If the price of petrol increases by 20%, by what percent should Mr. Brown reduce his consumption of petrol so that his expenditure on petrol remains the same?

X, Y, and Z can complete a work alone in 24, 36, and 18 days respectively. In how many days can X, Y and Z together complete 1/2 of the same work?

Former Retired Banker (1972–2000)Author has 5.5K answers and 2.2M answer viewsMay 18

X = 10 days Y = 10 + 8 days Z = 8 +5 days

X + Y in 10 days do 10/20 = 1/2 the work

Y + Z in 8 days do 8/24 = 1/3 of the work

Work remaining = 1–1/2 -1/3 = 1/6 of the work

This is done by Z in 5 days

So Z alone =30 days

Let Y alone take y days

1/y + 1/30 = 1/24

1/y = 1/24–1/30 = 6/720= 1/120

So Y alone = 120 days

Let X alone take x days

1/x + 1/120= 1/20

1/x = 1/20–1/120 = 5/120 = 1/24

So X alone = 24 days

X + Z in 1 day = 1/24 +1/30 = 54/720 = = 3/40

So X + Z take 40/3 days to do the complete work

75% of work will take them 3/4 X 40/3 = 10 days ANSWER

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Maths for school students

Let fraction of whole work, which is done by X in one day = x.

fraction of whole work, which is done by Y in one day = y.

fraction of whole work, which is done by Z in one day = z.

So, we have three set of equations from the given data:

20x + 20y + 0z = 1 ——————————- (1)

0x + 24y + 24z = 1 ———————————————- (2)

10x + 18y + 13z = 1 ————————————— (3)

Solving three equations:

x = Dx / D = ∣ ∣ ∣ ∣ ∣ 1 1 1 20 24 18 0 24 13 ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ 20 0 10 20 24 18 0 24 13 ∣ ∣ ∣ ∣ ∣

|12001242411813||2020002424101813|

= 100 / 2400 = 1/24.

Similarly, y = Dy /D = 20/2400 = 1/120

z = Dz / D = Pradeep Hebbar

23+ years of Structural Engineering & Math enthusiasmAuthor has 4K answers and 1.9M answer viewsMay 18

Let x x , y y and z z

respectively be the no of days required by

X X , Y Y and Z Z

to finish the work alone.

Part of work done by

X X , Y Y and Z Z per day is 1 x 1x , 1 y 1y , 1 z 1z respectively. X X and Y Y

together can complete a work in

20 20 days. Y Y and Z Z

together can complete the work in

24 24 days. 1 x + 1 y = 1 20 1x+1y=120 1 y + 1 z = 1 24 1y+1z=124 X X worked for 10 10 days and Y Y for 18 18 days. Z Z

alone completed the remaining work in

13 13 days 10× 1 x +18× 1 y +13× 1 z =1 10×1x+18×1y+13×1z=1

10\left(\dfrac{1}{x}+ \dfrac{1}{y}\right)+ 8 \left(\dfrac{1}{y}+\dfrac{

10\left(\dfrac{1}{x}+ \dfrac{1}{y}\right)+ 8 \left(\dfrac{1}{y}+\dfrac{

Related questions

A person sold an article at a profit of 15%. Had it been sold Rs 81 less, his loss would have been 12%. What is the cost price of the article?

X, Y, and Z can together complete a piece of work in 10 days; if Y does half of what X and Z together do in 1 day, in how many days can Y alone do the complete work?

स्रोत : www.quora.com

## [Solved] X and Y together can complete a piece of work in 18 days. If

Let ‘x’ and ‘y’ be the efficiencies of X and Y; According to the given condition; (x + y) × 18 = (3x/4 + 3y/2) × 15 &rArr

Home Quantitative Aptitude Time and Work Work Efficiency

## X and Y together can complete a piece of work in 18 days. If X and Y work 3/4th and 3/2nd of their efficiencies respectively, then the work will be completed in 15 days. In how many days X alone can complete the whole work?

45 days 36 days 30 days 54 days

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## Detailed Solution

Let ‘x’ and ‘y’ be the efficiencies of X and Y;

According to the given condition;

(x + y) × 18 = (3x/4 + 3y/2) × 15

⇒ 6x + 6y = 15x/4 + 15y/2

⇒ x : y = 2 : 3

∴ Total units of work = (2 + 3) × 18 = 90 units

∴ Time taken by X to complete the work alone = 90/2 = 45 days

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## More Work Efficiency Questions

Q1. If seven persons can build a house in 30 days, how long will it take three persons to build the same house, provided that they all work at the same rate?Q2. A, B and C can complete a work in 12, 16 and 24 days respectively. B and C worked together for 4 days then C left the work and A replaced him. In how many days will the remaining work be completed?Q3. P, Q, R can do a piece of work in 40 days, 90 days and 36 days, respectively. P started the work. Q joined him after 7 days. If R joined them after 8 days from the beginning, then for how many days did R work?Q4. A man can do a work in 20 days and a woman can do the same work in 30 days. In how many days will 2 men and 3 women do the work?Q5. 8 men or 12 women can do a piece of work in 24 days. In how many days can the work be done by 8 men and 12 women?Q6. Ronit and Hrithik can complete a work in 15 days and 35 days respectively. Hrithik started the work alone and joined by Ronit after the completion of

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of the work. Find the time taken to complete the work in this way:

Q7. 41 girls can complete a piece of work in 40 days. If x girls started the work and after 30 days 64 more girls joined them so that the whole work gets finished in the desired time, find the value of x.Q8. Rajat started a work alone and left after 10 days leaving 75% of the work for Simran. If Simran can complete the remaining work in 30 days, then find the time taken by Rajat and Simran together to complete 45% of the work.Q9. A can do a piece of work in 10 days while B can do the same work in 20 days. They start together but A leaves after three days. How many days will B take to complete the remaining work?Q10. X takes 5 days more than Y and 9 days more than Z to finish a piece of work. X and Y can do a piece of work together in the same time in which the Z alone can do the work. In how many days X finishes the work?

## More Time and Work Questions

Q1. If seven persons can build a house in 30 days, how long will it take three persons to build the same house, provided that they all work at the same rate?Q2. A, B and C can complete a work in 12, 16 and 24 days respectively. B and C worked together for 4 days then C left the work and A replaced him. In how many days will the remaining work be completed?Q3. Ram and Rahim together have Rs. 1210. If

13

of Ram's money is equal to

25

of Rahim's amount, then what is the amount (in Rs.) that Rahim has?

Q4. P, Q, R can do a piece of work in 40 days, 90 days and 36 days, respectively. P started the work. Q joined him after 7 days. If R joined them after 8 days from the beginning, then for how many days did R work?Q5. Pipe A can fill 50% of a tank in 4 hours and pipe B can completely fill the same tank in 12 hours. If both the pipes are opened at the same time, then in how much time will the empty tank be completely filled?Q6. A man can do a work in 20 days and a woman can do the same work in 30 days. In how many days will 2 men and 3 women do the work?Q7. A and B undertake to do a piece of work for Rs. 18,750. A can do it in 20 days and B can do it in 30 days. With the help of C, they finished it in 8 days. How much C should be paid for his work in proportion?Q8. 8 men or 12 women can do a piece of work in 24 days. In how many days can the work be done by 8 men and 12 women?Q9. A group of men can do a job in 25 days. But 10 men did not turn up for the job and the remaining men did the job in 30 days. The original number of men in group wasQ10. 10 workers working with same speed were deployed to construct a structure. 2 workers left on the 2nd day, another 2 left on the 3rd day and this went on till the work is completed. As a result 2 more days were needed to complete the work. Select the number of days that were needed if 10 workers worked for all days.

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Mohammed 2 month ago

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