Time and Work Problems with Solutions for Bank Exams

Time and Work Problems with Solutions for Competitive Exams: 

Q.6. A tyre has two punctures. The first puncture alone would have made the tyre flat in 9 minutes and the second alone would have done it in 6 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat ?

Solution:

1 minute’s work of both the $$ Punctures= \left({1\over9}+{1\over6}\right)={5\over18} $$

So, both the puncture will make the tyre $$ flat \ in = {18\over5}=3{3\over5}min $$

Q.7. 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 :

Solution:

(A+B+C)’s 1 day’s $$ work= \left({1\over24}+{1\over6}+{1\over12}\right)={7\over24} $$

So, A , B and C together will complete the $$ Job \ in = {24\over7}=3{3\over7}days $$

Q.8. A man can do a job in 15 days. His father takes 20 days and his son finishes it in 25 days. How long will they take to complete the job if they all work together ?

Solution:

1 day’s work of the three $$ persons = \left({1\over15}+{1\over20}+{1\over25}\right)={47\over300} $$

So, all the three together will complete the work $$ Work \ in = {300\over47}=6.4 \ days $$

Q.9. A man can do a piece of work in 5 days, but with the help of his son, he can do it in 3 days. In what time can the son do it alone ?

Solution: 

Son’s 1 day’s work = $$ Work = \left({1\over3}-{1\over5}\right)={2\over15} $$

∴  The son alone can do the work in  $$ Work \ in = {15\over2}=7{1\over2}days $$

Q.10.A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With the help of C, they did the job in 4 days only. Then, C alone can do the job in :

Solution: 

(A+B+C)’s 1 day’s $$ Work \  = {1\over4}$$

A’s 1 day’s $$ Work \  = {1\over16} $$

B’s 1 day’s $$ Work \  = {1\over12} $$

∴ C’s 1 day’s  $$ Work = {1\over4}-\left({1\over16}+{1\over12}\right)=\left({1\over4}-{7\over48}\right)={5\over48} $$

So, C alone can do the   $$ Work \ in   = {48\over9}=9{3\over5}days $$

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