# Work profit & loss

#### Question No 1

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 2

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 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

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.

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 6 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 7 John's income increased from$12000 to $14400. What is percentage increase in his income? #### Select the correct answer Solution! Increase in income = 14400 - 12000 = 2400 Percentage increase = (2400/12000)*100 = 20%. #### Question No 8 With an increase of 12% salary of Ali became Rs13440. What was his salary before increase? #### Select the correct answer 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 9 Ali sold a house at a loss of 15% for Rs. 382500. What was the cost price of the house? #### Select the correct answer 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 10 An estate agent sold a property at a profit of 10% for$825000. What was cost price of the property?

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

Now
825000 - (x/10) = x
8250000 - x = 10x
8250000 = 11x
x = 750000

Hence cost price of the property is $750000.. #### Question No 11 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? #### Select the correct answer 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 12 Cost price of a camera was$430 and it was sold at profit of 16%. What is its selling price?

Solution!
16% of 430 = (430*16)/100 = 68.8

Selling price = 430 + 68.8 = 498.8.

#### Question No 13

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 14

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..

What will be the selling price of an article that was bought for $1150 and sold at profit of 6%? #### Select the correct answer Solution! 6% of 1150 = (1150*6)/100 = 69 Selling price = 1150+69 = 1219. #### Question No 16 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 17 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 18 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 19

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 22

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

Solution!
C.P. of 1 orange = 350/100 = Rs. 3.50

S.P. of 1 orange = 48/12 = Rs. 4

Hence, Gain% = (0.50)/(3.50) * 100 = 100/7 %.

#### Question No 23

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 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..

A car was bought for $380000 four years ago and during these four year it price decreases by 12%. What is its value now? #### Select the correct answer Solution! 12% of 380000 (380000/100)*12 = 45600 Price of the car = 380000 - 45600 = 334400. #### Question No 26 By selling a Television for$572 Adam lost 12%. What was the cost price of the television?

Solution!
Let cost price of the television is x.
12% of x = 12x/100 = 3x/25

Now
(3x/25)+572 = x
3x + 14300 = 25x
14300 = 22x
x = 650

Hence cost price of the television is $650.. #### Question No 27 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 28 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? #### Select the correct answer 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.. #### Question No 29 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? #### Select the correct answer 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 30 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? #### Select the correct answer 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 31 John sold a house for$494500 at a profit of 15%. How much did he pay for it?

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

Now
494500 - (3x/20) = x
9890000 -3x = 20x
9890000 = 23x
x = 430000

Hence cost price of the house is $430000.. #### Question No 32 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 #### Select the correct answer 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 33 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 #### Select the correct answer 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 34 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 #### Select the correct answer 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.. #### Question No 35 What will be the selling price of an article that was bought for$350 and sold at a loss of 14%?

Solution!
14% of 350
(350*14)/100 = 49

selling price of the article = 350 - 49 = 301.

#### Question No 36

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?

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 37

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 38

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 39

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

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%.

A shopkeeper bought an article for $120 and sold at profit of 10%. What is selling price of the article? #### Select the correct answer Solution! 10% of 120 = (120*10)/100 = 12 Selling price = 120+12 = 132. #### Question No 41 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? #### Select the correct answer 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 42 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 #### Select the correct answer 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 43 On selling 17 balls at$720, there is a loss equal to the cost price of 5 balls.The cost price of a ball is

Solution!
(C.P. of 17 balls) - (S.P. of 17 balls) = (C.P. of 5 balls)

C.P. of 12 balls = S.P. of 17 balls = $720 C.P. of 1 ball =$60.

#### Question No 44

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 45

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 46

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 47

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 48

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 49

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 51

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%.

An article was bought for $300 and sold at a loss of 8%. What is the selling price of the article? #### Select the correct answer Solution! 8% of 300 = (300*8)/100 = 24 Selling price = 300-24 = 276. #### Question No 53 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? #### Select the correct answer 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 54 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 #### Select the correct answer 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 55 If selling price is doubled, the profit triples. Find the profit percent. #### Select the correct answer 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%. #### Question No 56 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. #### Select the correct answer 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 57 Price of a car increased from$400000 to $420000. What is the percentage increase? #### Select the correct answer Solution! Increase in price = 420000 - 400000 = 20000 Percentage increase = (20000/400000)*100 = 5%. #### Question No 58 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 #### Select the correct answer 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 59 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 60

25 tailors can make 35 dresses in 1 day. How many dresses can 6 tailors make in 5 days?