## EXERCISE 11

Question 1

**A can do of the work in 12 days . In how many days can he complete of the work ?**

Sol :

⇒A can do of work in 12 days

⇒ A can do 1 work in days And [Mutiplying both side by 3/4]

⇒ A can do work in days [Multiplying both side by 1/8]

days

= 2 days

Question 2

**Tanu can do a piece of work in 24 days and Manisha can do it in 30 days . How long will they take to do the work working together ?**

Sol :

⇒Tanu can do a piece of work in 24 days

⇒So Tanu’s one day work

⇒Manisha can do the same work in 30 days

⇒So Manisha’s one day work

⇒We know that

⇒Tanu and Manisha’s one day work = Tanu’s one day work + Manisha’s one day work

[Taking LCM]

⇒Tanu and Manisha’s one day work

⇒Total time required for completing work

⇒So Tanu and Manisha can complete the same work in days.

Question 3

**A and B can polish the floors of a building in 18 days . A alone can do of this job in 4 days . in how many days can B alone polish the floors ?**

Sol :

⇒A alone complete whole work in = 24 days

⇒A’s one day work

⇒(A and B)’s one day work

⇒Also , (A+B)’s one day work = A’s one day work + B’s one day work

⇒

⇒

⇒

⇒x = 72

72 days

Question 4

**A and B can weave a certain number of baskets in 12 days and 15 days respectively . They work together for 5 days and then B leaves . In how many days will A finish the rest of the work ?**

Sol :

⇒A’s one day work

⇒B’s one day work

⇒(A + B)’s one day work = A’s one day work + B’s one day work

⇒(A + B)’s one day work

⇒They work together for 5 days

⇒Remaining work

⇒A can complete all work in 12 days . So , remaining work can be done in days

= 3 days

Question 5

**A , B and C working together take 8 min . to address a pile of envelopes . A and B together would take 10 min ; A and C together would take 15 min . How long would each take working alone ?**

Sol :

⇒(A + B + C)’s one unit work

⇒(A + B)’s one unit work

⇒(A + C)’s one unit work

⇒C’s one unit work = (A + B + C)’s one unit work – (A + B)’s one unit work

∴C alone take 40 min

⇒B’s one unit work = (A + B + C)’s one unit work – (A + C)’s one unit work

∴B alone take min

⇒A’s one unit work = (A + B + C)’s one unit work – B’s one unit work – C’s one unit work

∴A alone take 24 min

A→24 min ; B→ min ; C→40 min

Question 6

**A and B can do a piece of work in 6 days and 4 days respectively . A started the work ; worked at it for 2 days and then was joined by B . Find the total time taken to complete the work .**

Sol :

⇒A’s one day work

⇒B’s one day work

⇒A’s 2 days work

⇒Remaining work

..(i)

⇒(A+B)’s one day work = A’s one day work + B’s one day work

or

⇒Total time required to complete work together

⇒Time to complete the remaining work together ..(ii)

⇒Total time required to complete work = A’s alone working time + (A+B)’s working together time

Question 7

**780 is paid for a task which A can do in 6 days , B in 8 days and C in 4 days . If all work together , how much money should each receive ?**

Sol :

⇒A’s one day work

⇒B’s one day work

⇒C’s one day work

∴Ratio of shares of money of A , B and C = Ratio of their one day work

[L.C.M of 6 , 8 and 24]

= 4 : 3 : 6

∴Sum of the ratios = 4 + 3 + 6 = 13

⇒A’s share = 240

⇒B’s share = 180

⇒C’s share = 360

A→240 , B→180 , C→360

Question 8

**X works thrice as fast as Y . If Y alone can complete a job in 18 days , find how ,many days will X and Y together take to complete the job .**

Sol :

⇒Y’s one day work

A.T.Q

⇒3X=Y

⇒

⇒

⇒X=6

⇒X’s one day work

⇒(X+Y)’s one day work = X’s one day work + Y’s one day work

⇒Total time required by (X+Y) to complete work or days

Question 9

**A can do a job in 20 days , B in 30 days and C in 60 days . If A is helped by B and C on every third day , then in how many days will the job be finished ?**

Sol :

⇒A’s one day work ..(i)

⇒(A+B+C)’s one day work = A’s one day work + B’s one day work + C’s one day work

..(i)

⇒According to question, A work starting two days alone and on every third day all together work .

Total time to complete work = 1st day + 2nd day + 3rd day

1 and 2 day equal to (i) and 3 day equal to (ii)

Which means in 3 days 1/5 work is completed

= 15 days to complete whole work

Question 10

**Sonia can copy 50 pages in 10 hours . Priya and Sonia can copy 300 pages in 40 hours . In how much time can Priya copy 30 pages ?**

Sol :

⇒Sonia in 10 hours can copy 50 pages

∴In 1 hour sonia can copy pages

⇒Priya and Sonia together in 40 hours can copy 300 pages

∴Priya and Sonia together in 1 hours can copy pages

⇒Priya’s 1 hour work = Priya and Sonia together in 1 hours work – Sonia’s 1 hour work

⇒Number of hours required to complete the work

= 12 hours

Question 11

**A tap can fill a cistern in 15 minutes and another can empty it in 18 minutes . Find in how many minutes the tank will be filled up ?**

Sol :

⇒Tank filled by tap in one hour part

⇒Tank empty by tap in one hour part

⇒Tank filled in one hour when both taps are open

= 90 mins the tank will be filled up

Question 12

**Two taps can fill a cistern in 15 hours and 20 hours respectively . A third tap can empty it in 30 hours . How long will they take to fill the cistern if all the taps are opened ?**

Sol :

⇒Tank filled by first tap in one hour part

⇒Tank filled by second tap in one hour part

⇒Tank empty by third tap in one hour part

⇒Tank filled in one hour when all three taps are open

= 12 hours take the tank to fill up

Question 13

**Two taps running together can fill a bath in 4 minutes , which is filled by one of the taps by itself in 7 minutes . How long would it take if the other pipe is running by itself ?**

Sol :

⇒Bathtub filled by (1st + 2nd) taps in one hour part

⇒Bathtub filled by first tap in one hour part

⇒Bathtub filled by (1st + 2nd) taps in one hour = time taken by 1st tap in one hour + time taken by 2nd tap in one hour

⇒

⇒

⇒

⇒

Time taken by Second tap minutes

Question 14

**A cistern can be filled by 3 taps A, B and C when turned on separately in 12 min , 10 min and 15 min respectively . If all are turned on together for minutes and if B and C are then turned off , how much time will A alone take to fill the cistern ?**

Sol :

⇒Time taken when all 3 taps are open for a unit time = Tap A open for unit time + Tap B open for unit time + Tap C open for unit time

A.T.Q

⇒All are turned for minutes

⇒Remaining cistern to be filled

⇒Tap A alone fill the remaining cistern [1/3 of 12min]

= 4 minutes