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

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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

## If A andB 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 ?

**A**

## 30 days

**B**

## 60 days

**C**

## 15 days

**D**

## 45 days

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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.

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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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Answered by Ansh Keer

Author has 3.1K answers and 814.2K answer viewsMay 20

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

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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?

Ranjan Karnad

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

Answered by

Niladri Shekhar Mandal

Author has 2K answers and 198.5K answer viewsMay 19

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{

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## [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

## Question

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## 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

## Answer (Detailed Solution Below)

Option 1 : 45 days Crack SSC with

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## Detailed Solution

Download Solution PDF

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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