# Work profit & loss

#### Question No 1

A, B and C can complete a piece of work in 24, 6 and 12 days respectively.Working together,they will complete the same work in

Solution!
As we know that
If A can do a piece of work in n days, then A's 1 day's work = 1/n

(A + B + C)'s 1 day's work = (1/24 + 1/6 + 1/12) = 7/24

If A's 1 day's work = 1/n then,
A can finish the work in 'n' days.

So, all the three together will complete the job in (24/7) days..

#### Question No 3

A does 80% of a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work?

Solution!
Whole work is done by A in (20 * 5/4) = 25 days

Now, (1 - 4/5) i.e., 1/5 work is done by A and B in 3 days.

Whole work will be done by A and B in (3 x 5) = 15 days.

A's 1 day's work = 1/25
(A + B)'s 1 day's work = 1/15

So, B's 1 day's work = (1/15 - 1/25) = 4/150 = 2/75

Hence, B alone would do the work in 75/2 = 37.5 days..

#### Question No 4

Ali bought a house for $450000 and sold it for$500000. What is his profit percentage?

Solution!
Profit = 500000-450000 = 50000

Profit percentage= (50000/450000)*100 = 11.11%.

C.P. of 1 ball = $60. #### Question No 6 25 tailors can make 35 dresses in 1 day. How many dresses can 6 tailors make in 5 days? #### Select the correct answer Solution! Let x dresses can be made. As dresses are directly proportional to tailors and days so x/35 = (6/25)*(5/1) x = 42 Hence 42 dresses can be made by 6 tailors in 5 days.. #### Question No 7 By selling an article for$200 shopkeeper looses 20%. What is cost price of the article?

Solution!
Let cost price of the article is x.

20% of x = (x*20)/100 = x/5

Now
(x/5) + 200 = x
x+1000 = 5x
4x = 1000
x = 250

Hence cost price of the article is 250..

#### Question No 8

Price of a car increased from $400000 to$420000. What is the percentage increase?

Solution!
Increase in price = 420000 - 400000
= 20000

Percentage increase = (20000/400000)*100
= 5%.

#### Question No 10

With an increase of 12% salary of Ali became Rs13440. What was his salary before increase?

Solution!
Let before increase Ali's salary was x.
12% of x = 12x/100 = 3x/25

Now
13440 - 3x/25 = x
336000 - 3x = 25x
336000 = 28x
x = 12000

Hence Ali's salary before increase was Rs. 12000.

#### Question No 11

A and B can do a job together in 7 days. A is 7/4 times as efficient as B.The same job can be done by A alone in

Solution!
(A's 1 day's work) / (B's 1 day's work) = 7/4

Let A's and B's 1 day's work be 7x and 4x respectively.

Then,
7x + 4x = 1/7
11x = 1/7
x = 1/77

Hence, A's 1 day's work = (1/77 * 7) = 1/11.

#### Question No 13

Value of a house decreased from $250000 to$200000. What is the percentage decrease in the value?

Solution!
Decrease in value of house = 250000 - 200000 = 50000

Percentage decrease = (50000/250000)*100 = 20%.

#### Question No 14

Price of a fuel increased by 10% during budget. If its price before budget was Rs. 55 per liter what is its price after the budget?

Solution!
10% of 55 = (55*10)/100 = 5.5

Price of fuel after butget = 55+5.5 = 60.5.

#### Question No 15

A can do a piece of work in 4 hours; B and C together can do it in 3 hours,while A and C together can do it in 2 hours.How long will B alone take to do it?

Solution!
A's 1 hour's work = 1/4

(B + C)'s 1 hour's work = 1/3

(A + C)'s 1 hour's work = 1/2

(A + B + C)'s 1 hour's work = (1/4 + 1/3) = 7/12

B's 1 hour's work = (7/12 - 1/2) = 1/12

Hence, B alone will take 12 hours to do the work..

#### Question No 16

The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is

Solution!
Let
C.P. of each article be Re. 1 C.P. of x articles = Rs. x.

S.P. of x articles = Rs. 20.

Profit = Rs. (20 - x)

So, (20-x)/x * 100 = 25
2000 - 100x = 25x
125x = 2000

Hence, x = 16.

#### Question No 17

A can do a certain work in the same time in which B and C together can do it.If A and B together could do it in 10 days and C alone in 50 days,then B alone could do it in

Solution!
(A + B)'s 1 day's work = 1/10

C's 1 day's work = 1/50

(A + B + C)'s 1 day's work = (1/10 + 1/50) = 6/50 = 3/25...(1)

A's 1 day's work = (B + C)'s 1 day's work .... (2)

From (1) and (2), we get
2 * (A's 1 day's work) = 3/25

A's 1 day's work = 3/50

So, B's 1 day's work (1/10 - 3/50) = 2/50 = 1/25

Hence, B alone could do the work in 25 days..

#### Question No 18

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?

Solution!
1 woman's 1 day's work =1/70

1 child's 1 day's work =1/140

(5 women + 10 children)'s 1 day's work = (5/70 + 10/140) = (1/14 + 1/14) = 1/7

Hence, 5 women and 10 children will complete the work in 7 days..

#### Question No 19

A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 392, what was his profit?

Solution!
C.P. = (100/122.5) * 392
= (1000/1225) * 392
= Rs. 320

Hence, Profit = Rs. (392 - 320) = Rs. 72..

#### Question No 20

If selling price is doubled, the profit triples. Find the profit percent.

Solution!
Let
C.P. be Rs. x and S.P. be Rs. y.

Then,
3(y - x) = (2y - x)
y = 2x

Profit = Rs. (y - x) = Rs. x

Profit % = (x/x)*100 = 100%.

Cost price of a camera was $430 and it was sold at profit of 16%. What is its selling price? #### Select the correct answer Solution! 16% of 430 = (430*16)/100 = 68.8 Selling price = 430 + 68.8 = 498.8. #### Question No 22 Alfred buys an old scooter for Rs. 4700 and spends Rs. 800 on its repairs. If he sells the scooter for Rs. 5800, his gain percent is #### Select the correct answer Solution! Cost Price (C.P.) = (4700 + 800) = Rs. 5500 Selling Price (S.P.) = Rs. 5800 Gain = (S.P.) - (C.P.) = (5800 - 5500) = Rs. 300 Gain % = (300/5500) * 100 = 60/5 %. #### Question No 23 A car was bought for$380000 four years ago and during these four year it price decreases by 12%. What is its value now?

Solution!
12% of 380000
(380000/100)*12 = 45600

Price of the car = 380000 - 45600 = 334400.

#### Question No 24

Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is

Solution!
Ratio of times taken by Sakshi and Tanya = 125/100 = 5/4

Suppose Tanya takes x days to do the work.

5/4 = 20/x
x = (4*20)/5

x = 16 days.

Hence, Tanya takes 16 days to complete the work..

#### Question No 25

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

Solution!
(20 x 16) women can complete the work in 1 day.

So, woman's 1 day's work = 1/320

(16 x 15) men can complete the work in 1 day.

So, 1 man's 1 day's work = 1/240

So, required ratio = (1/240) / (1/320)
= (1/3) / (1/4) = 4/3.

#### Question No 26

9 excavators working 10 hours a day remove 2500 cubic feet of earth in 3 days. How many excavators working 6 hours a day are required to remove 5000 cubic feet of earth in 2 days?

Solution!
Let x excavators are required.
As excavators are inversely proportional to hours and days and directly proportional to work progress so
x/9 = (10/6)*(5000/2500)*(3/2)
x = 45

Hence 45 excavators are required to remove 5000 cubic feet of earth..

#### Question No 27

In a fort there is enough food sufficient for 1200 men for 10 days. How long the food would have last for if there would have been 1000 men.

Solution!
Let food will last for x days.
As men and days are inversely proportional to each other so
x/10 = 1200/1000
x = 12

Hence food will last for 12 days if there were 1000 men..

#### Question No 28

John's income increased from $12000 to$14400. What is percentage increase in his income?

Solution!
Increase in income = 14400 - 12000 = 2400

Percentage increase = (2400/12000)*100 = 20%.

#### Question No 29

A can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?

Solution!
B's 10 day's work = (1/15 * 10) = 2/3

Remaining work = (1 - 2/3) = 1/3

Now, 1/18 work is done by A in 1 day.

Hence, 1/3 work is done by A in (18 * 1/3) = 6 days..

#### Question No 30

A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days?

Solution!
Ratio of times taken by A and B = 100/130 = 10/13

Suppose B takes x days to do the work.

Then, 10/13 = 23/x
x = (23*13)/10
x = 299/10

A's 1 day's work = 1/23

B's 1 day's work = 10/299

(A + B)'s 1 day's work = (1/23 + 10/299) = 23/299 = 1/13

Therefore, A and B together can complete the work in 13 days..

#### Question No 31

If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be

Solution!
Let, 1 man's 1 day's work = x
and 1 boy's 1 day's work = y

Then, 6x + 8y = 1/10
and 26x + 48y = 1/2

Solving these two equations, we get
x = 1/100
and y = 1/200

(15 men + 20 boy)'s 1 day's work = (15/100 + 20/200) = 1/4

Hence, 15 men and 20 boys can do the work in 4 days..

#### Question No 32

Ali sold a house at a loss of 15% for Rs. 382500. What was the cost price of the house?

Solution!
Let cost price of the house is x.
15% of x = 15x/100 = 3x/20

Now
(3x/20)+382500 = x
3x + 7650000 = 20x
7650000 = 17x
x = 450000
Hence cost price of the house is Rs. 450000.

#### Question No 33

A can finish a work in 24 days, B in 9 days and C in 12 days. B and C start the work but are forced to leave after 3 days. The remaining work was done by A in

Solution!
(B + C)'s 1 day's work = (1/9 + 1/12) = 7/36

Work done by B and C in 3 days = (7/36 * 3)
= 7/12

Remaining work = (1 - 7/12)
= 5/12

Now, 1/24 work is done by A in 1 day.

So, 5/12 work is done by A in (24 * 5/12) = 10 days..

What will be the selling price of an article that was bought for $475 and sold at a loss of 12%? #### Select the correct answer Solution! 12% of 475 =(475*12)/100 = 57 Selling price = 475-57 = 418. #### Question No 35 A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg.His profit percent is #### Select the correct answer Solution! C.P. of 56 kg rice = (26 x 20 + 30 x 36) = (520 + 1080) = Rs. 1600 S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680 Hence, Gain = (80/1600)*100 = 5%. #### Question No 36 A man buys a cycle for Rs. 1400 and sells it at a loss of 15%. What is the selling price of the cycle? #### Select the correct answer Solution! S.P. = 85% of Rs. 1400 =(85/100)*1400 =Rs. 1190. #### Question No 37 A takes twice as much time as B or thrice as much time as C to finish a piece of work.Working together,they can finish the work in 2 days.B can do the work alone in #### Select the correct answer Solution! Suppose A, B and C take x, x/2, x/3 days respectively to finish the work. Then, (1/x + 2/x + 3/x) = 1/2 6/x = 1/2 x=12 So, B takes (12/2) = 6 days to finish the work.. #### Question No 38 What will be the selling price of an article that was bought for$1150 and sold at profit of 6%?

Solution!
6% of 1150
= (1150*6)/100 = 69

Selling price = 1150+69 = 1219.

#### Question No 39

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?

Solution!
Let, 1 man's 1 day's work = x
and
1 woman's 1 day's work = y

Then, 4x + 6y = 1/8 nd 3x + 7y = 1/10

Solving the two equations, we get
x = 11/400
y = 1/400

So, One woman's 1 day's work = 1/400

10 women's 1 day's work = (1/400 * 10) = 1/40

Hence, 10 women will complete the work in 40 days..

#### Question No 40

Some articles were bought at 6 articles for Rs. 5 and sold at 5 articles for Rs. 6. Gain percent is

Solution!
Suppose, number of articles bought =L.C.M. of 6 and 5
= 30

C.P. of 30 articles = (5/6) * 30 = Rs. 25

S.P. of 30 articles = (6/5)*30
= Rs. 36

Hence, Gain % = (11/25) * 100 = 44%.

#### Question No 41

A is thrice as good as a workman as B and therefore is able to finish a job in 60 days less than B.Working together,they can do it in

Solution!
Ratio of times taken by A and B = 1/3

The time difference is (3 - 1) 2 days while B take 3 days and A takes 1 day.

If difference of time is 2 days, B takes 3 days.

If difference of time is 60 days, B takes (3/2 * 60) = 90 days

So, A takes 30 days to do the work.

A's 1 day's work = 1/30

B's 1 day's work = 1/90

(A + B)'s 1 day's work = (1/30 + 1/90) = 4/90 = 2/45

Hence, A and B together can do the work in 45/2 = 22.5 days.

#### Question No 42

Price of an article increased from $50 to$55. What is the percentage increase?

Solution!
Increase in price = 55-50 = 5
Percentage increase = (5/50)*100
=10%.

#### Question No 43

A group of workers can do a piece of work in 24 days. However as 7 of them were absent it took 30 days to complete the work. How many people actually worked on the job to complete it?

Solution!
Let x workers are required to complete the job.
As workers and days are inversely proportional to each other so
(x-7)/x = 24/30
30x - 210 = 24x
6x = 210
x = 35

Hence 35 workers are required to complete the job in time..

What will be the selling price of an article that was bought for $350 and sold at a loss of 14%? #### Select the correct answer Solution! 14% of 350 (350*14)/100 = 49 selling price of the article = 350 - 49 = 301. #### Question No 45 In a ship the provisions are sufficient for 800 men for 50 days. How long will these be sufficient for if there would have been 200 more men? #### Select the correct answer Solution! Let provisions will be sufficient for 200 men for x days. As men and days are inversely proportional to each other so x/50 = 800/1000 x = 40 Hence provisions will be sufficient for 200 men for 40 days.. #### Question No 46 Price of an article decreased from$70 to $56. What is the percentage decrease? #### Select the correct answer Solution! Decrease in price = 70-56 = 14 Percentage decrease = (14/70)*100 = 20%. #### Question No 47 A shopkeeper bought an article for$120 and sold at profit of 10%. What is selling price of the article?

Solution!
10% of 120
= (120*10)/100 = 12

Selling price = 120+12 = 132.

#### Question No 48

By selling a car for Rs. 495000 an agent gains 10%. What was his cost?

Solution!
Let cost price of the car is x.
10% of x = 10x/100 = x/10

Now
495000 - (x/10) = x
4950000 - x = 10x
4950000 = 11x
x = 450000.

#### Question No 49

A vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 20%?

Solution!
C.P. of 6 toffees = Re. 1

S.P. of 6 toffees = 120% of Re. 1 = Rs. 6/5

For Rs. 6/5,
toffees sold = 6.

For Re. 1, toffees sold = (6 * 5/6) = 5.

#### Question No 50

A works twice as fast as B.If B can complete a work in 12 days independently,The number of days in which A and B can together finish the work in

Solution!
Ratio of rates of working of A and B = 2/1

So, ratio of times taken = 1/2

B's 1 day's work = 1/12

A's 1 day's work = 1/6
(2 times of B's work)

(A + B)'s 1 day's work = (1/6 + 1/12) = 1/4

So, A and B together can finish the work in 4 days..

#### Question No 52

X can do a piece of work in 40 days.He works at it for 8 days and then Y finished it in 16 days.How long will they together take to complete the work?

Solution!
Work done by X in 8 days = (1/40 * 8)
= 1/5

Remaining work = (1 - 1/5)
4/5

Now, 4/5 work is done by Y in 16 days.

Whole work will be done by Y in (16 * 5/4)
= 20 days

So,
X's 1 day's work = 1/40
Y's 1 day's work = 1/20

(X + Y)'s 1 day's work = (1/40 + 1/20) = 3/40

Hence, X and Y will together complete the work in 40/3 days.

#### Question No 54

A salesman bought a pen for Rs. 100 and sold it for Rs. 110. What is his profit percent?

Solution!
Profit = 110 - 100 = 10

Profit percentage = (10/100)*100 = 10%.

#### Question No 55

A farmer bought a cow for Rs. 14000 and sold it for Rs. 15400. Find his profit percentage.

Solution!
Profit = 15400 - 14000 = 1400

Profit percentage = (1400/14000)*100 = 10%.

#### Question No 56

A can do a work in 15 days and B in 20 days.If they work on it together for 4 days,then the fraction of the work that is left is

Solution!
A's 1 day's work = 1/15

B's 1 day's work = 1/20

(A + B)'s 1 day's work = (1/15 + 1/20) = 7/60

(A + B)'s 4 day's work = (7/60 * 4) = 7/15

Therefore, Remaining work = (1 - 7/15) = 8/15.

#### Question No 58

An article was bought for \$300 and sold at a loss of 8%. What is the selling price of the article?

Solution!
8% of 300
= (300*8)/100 = 24

Selling price = 300-24 = 276.

#### Question No 59

A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in

Solution!
(A + B + C)'s 1 day's work = 1/6

(A + B)'s 1 day's work = 1/8

(B + C)'s 1 day's work = 1/12

So, (A + C)'s 1 day's work = (2* 1/6) - (1/8 + 1/12)
= (1/3 - 5/24) = (3/24) = 1/8

So, A and C together will do the work in 8 days..

#### Question No 60

100 oranges are bought at the rate of Rs. 350 and sold at the rate of Rs. 48 per dozen.The percentage of profit or loss is