第11章时间和工作–练习11.1 |套装1
问题15. A和B可以分别在6天和4天之内完成一件工作。 A开始工作，进行了2天的工作，然后由B加入。找到完成工作所需的总时间。
解决方案：
Given:
A can do a piece of work in = 6 days
A’s 1 day work = 1/6
B can do a piece of work in = 4 days
In 2 days the work completed by A = 2 × 1/6 = 1/3 part of work
Remaining work = 1 – 1/3
= (3-1)/3
= 2/3
A and B can finish the remaining work in = (2/3)/(1/6 + 1/4)
= (2/3)/(5/12)
= (2×12)/(3×5)
= 8/5 days
Therefore,
Total time taken to complete the work by A and B = 2 + 8/5
= (10+8)/5 = 18/5
= 3 3 days.
5
问题16。6个人可以在7天内完成建筑物中的电气安装。 21个男人从事这项工作需要多少天?
解决方案：
Given:
6 men can complete the job in = 7 days
1 man can complete the job in = 6 × 7 = 42 days
Therefore,
21 men can complete the job in = 42/21 = 2 days
问题17：8个人可以在9天内完成一件工作。 6个人将在几天内完成?
解决方案：
Given:
8 men can do a piece of work = 9 days
1 man can complete a piece of work in = 8 × 9 = 72 days
Therefore,
6 men can complete the work in = 72/6 = 12 days
问题18. Reema在25天内编织了35个篮子。她将在几天内编织55个篮子?
解决方案：
Given:
Reema weaves 35 baskets in = 25 days
Time taken by Reema to weave 1 basket = 25/35
Therefore,
Time taken by Reema to weave 55 baskets = 25/35 × 55
= 5/7 × 55
= 275/7
= 39 2 days.
7
问题19. Neha在14小时内键入75页。她将在20小时内键入多少页?
解决方案：
Given:
Number of pages Neha can type in 14 hours = 75 pages
Number of pages Neha can type in 1 hour = 75/14
Therefore,
Number of pages Neha can type in 20 hours = 20 × 75/14
= 750/7
= 107 1 pages.
7
问题20.如果12个男孩在7天内收入840卢比，那么15个男孩在6天内收入会是多少?
解决方案：
Given:
Earning of 12 boys in 7 days = Rs 840
Earning of 12 boys in 1 day = Rs 840/7
= Rs 120
Earning of 1 boy in 1 day = 120/12 = Rs 10
Earning of 1 boy in 6 days = 10 × 6 = Rs 60
Therefore
Earning of 15 boys in 6 days = 60 × 15 = Rs 900
问题21.如果25位男性在10天内赚取1000卢比，那么15位男性在15天内能赚多少钱?
解决方案：
Given:
In 10 days 25 men can earn = Rs.1000
In 1 day 25 men can earn = 1000/10 = Rs 100
In 1 day 1 man can earn = 100/25 = Rs 4
In 15 days 1 man can earn = 15 × 4 = Rs 60
Therefore,
In 15 days 15 men can earn = 60 × 15 = Rs 900
问题22：阿舒每天工作8个小时，可以在18天内复印一本书。他一天应该工作几小时才能在12天内完成工作?
解决方案：
Given:
Working 8 hours a day, Ashu can complete a work in = 18 days
Working 1 hour a day, Ashu can complete the work in = 18 × 8 = 144 days
Therefore,
Number of hours Ashu should work to complete the work in 12 days = 144/12 = 12 hours/day
问题23.如果9个女孩可以在3个小时内准备135个花环，那么需要多少女孩在1小时内准备270个花环?
解决方案：
Given:
In 3 hours, 9 Girls can prepare = 135 garlands
In 1 hour, 9 girls can prepare = 135/3 = 45 garlands
In 1 hour, 1 girl can prepare = 45/9 = 5 garlands
Therefore,
In 1 hour, Number of girls required to prepare 270 garlands = 270/5 = 54 girls
问题24.一个水箱可以在8小时内一次装满水，然后在4小时内再次装满水箱。如果两个水龙头一起打开，将水箱注满水需要多长时间?
解决方案：
Given:
A cistern can be filled by one tap in = 8 hours
A cistern filled by one tap in 1 hour = 1/8
Another cistern can be filled in = 4 hours
Cistern filled by another tap in 1 hour = 1/4
Total cistern filled in 1 hour = 1/4 + 1/8
= (2+1)/8
= 3/8
Therefore,
Cistern can be filled when both the taps are opened together in = 8/3 = 223 hours
问题25.两个龙头A和B可以分别在10小时和15小时内填充高架水箱。两个水龙头均打开4小时，然后关闭B。 A将需要多少时间来填充剩余的油箱?
解决方案：
Given:
Tap A can fill the tank in = 10 hours
Tap A can fill the tank in 1 hour = 1/10
Tap B can fill the tank in = 15 hours
Tap B can fill the tank in 1 hour = 1/15
Both taps together can fill the tank in 1 hour = 1/10 + 1/15
= (3+2)/30 = 5/30
= 1/6
Both taps together can fill the tank in 4 hours = 4 × 1/6 = 2/3
Remaining tank to be filled = 1 – 2/3
= (3-2)/3
= 1/3
Therefore,
Time taken by A to fill the remaining tank = (1/3)/(1/10)
= 10/3
= 3 1 hours.
3
问题26.管道可以在10个小时内装满水箱。由于底部泄漏，它会在12小时内充满。水箱装满后，泄漏会在多少时间内将其清空?
解决方案：
Given:
When there is no leakage A pipe can fill the cistern in = 10 hours
In 1 hour without leakage A pipe can fill the cistern in = 1/10 hours
When there is leakage cistern gets filled in = 12 hours
In 1 hour, when there is leakage cistern gets filled in = 1/12 hours
In 1 hour, due to leakage cistern gets filled to = 1/10 – 1/12
= (12-10)/120
= 2/120
= 1/60 part
Therefore,
Due to leakage the cistern gets emptied in = 1/(1/60) = 60 hours.
问题27.水箱有两个入口A和B，分别可以在12小时和15小时内充满水。出口可以在10小时内排空整个水箱。如果在空水箱中将所有三个管道一起打开，它们将花费多少时间才能完全充满水箱?
解决方案：
Given:
Inlet A can fill the cistern in = 12 hours
Inlet A can fill the cistern in 1 hour = 1/12
Inlet B can fill the cistern in = 15 hours
Inlet B can fill the cistern in 1 hour = 1/15
Outlet pipe can empty the cistern in = 10 hours
Outlet pipe can empty the cistern in 1 hour = 1/10
So we have, (1/12 + 1/15) – 1/10
= (9/60) – 1/10
= (9-6)/60
= 3/60
= 1/20 part
Therefore,
When all 3 pipes are opened together to empty the cistern, time taken to fill the cistern completly = 1/(1/20) = 20 hours
问题28.水箱可在4小时内用水龙头装满，并在6小时内用出口管将其装满。如果水龙头和水管一起打开，将水箱注满水需要多长时间?
解决方案：
Given:
Inlet tap can fill a cistern in = 4 hours
Inlet tap can fill a cistern in 1 hour = 1/4
Outlet tap can empty the cistern in = 6 hours
Outlet tap can empty the cistern in 1 hour = 1/6
Work done by both pipe in 1 hour = (1/4 – 1/6)
= (3-2)/12
= 1/12
Therefore,
When both tap and pipe are opened together the cistern can be filled in = 1/(1/12) = 12 hours.