# Work profit & loss

#### Question No 1

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

#### Select the correct answer

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 2

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 3

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

#### Select the correct answer

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 4

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 5

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

#### Select the correct answer

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

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

#### Question No 7

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

#### Select the correct answer

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..

#### Select the correct answer

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 14

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 15

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 16

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..

#### Select the correct answer

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

#### Select the correct answer

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

Now
(3x/20) + 476 = x
3x+9520 = 20x
9520 = 17x
x = 560

#### Select the correct answer

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

Selling price = 120+12 = 132.

#### Question No 23

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

#### Select the correct answer

Solution!
Profit = 500000-450000 = 50000

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

#### Question No 24

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

#### Select the correct answer

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 25

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 26

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 27

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.

#### Select the correct answer

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

Price of the car = 380000 - 45600 = 334400.

#### Question No 31

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..

#### Select the correct answer

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

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

#### Question No 34

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

#### Select the correct answer

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

#### Question No 35

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 36

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 38

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 39

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?

#### Select the correct answer

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 40

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

#### Select the correct answer

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 41

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 42

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

#### Select the correct answer

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 43

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 44

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

#### Select the correct answer

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 45

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

#### Select the correct answer

Solution!
Profit = 15400 - 14000 = 1400

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

#### Question No 47

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.

#### Select the correct answer

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 56

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

#### Select the correct answer

Solution!
Profit = 110 - 100 = 10

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

#### Question No 57

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?

#### Select the correct answer

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 58

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 59

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?

#### Select the correct answer

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 60

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?

#### Select the correct answer

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

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