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

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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?

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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?

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Solution!
Profit = 500000-450000 = 50000

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

Select the correct answer

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?

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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?

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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

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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?

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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?

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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?

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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

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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

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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?

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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?

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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.

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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%.

Select the correct answer

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

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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?

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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?

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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.

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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?

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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?

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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?

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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

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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?

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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

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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..

Select the correct answer

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?

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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

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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

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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?

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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?

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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..

Select the correct answer

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?

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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%?

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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

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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?

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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?

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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.

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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

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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?

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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

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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

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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 %.
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