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

(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..

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

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.

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

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..

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?

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..

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

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..

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

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.

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

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..

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

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..

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?

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..

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?

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.

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

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.

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

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 %.

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

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%.

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

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%.

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

(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..

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

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..

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?

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..

By selling a Television for $572 Adam lost 12%. What was the cost price of the television?

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..

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?

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..

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?

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..

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

(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.

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

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.

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?

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..

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?

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..

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?

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..

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?

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..

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

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..

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

(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..

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.

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..

An estate agent sold a property at a profit of 10% for $825000. What was cost price of the property?

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..

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?

(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.

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

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.