1. A and B can together finish a work 30 days. They worked together for 20 days and then B left. After another 20 days, A finished the remaining work. In how many days A alone can finish the work?
a) 40
b) 50
c) 54
d) 60
Explanation:
$$\eqalign{ & \left( {{\text{A + B}}} \right){\text{'s}}\,{\text{20}}\,{\text{day's}}\,{\text{work}} \cr & = {\frac{1}{{30}} \times 20} = \frac{2}{3} \cr & {\text{Remaining}}\,{\text{work}} \cr & = {1 - \frac{2}{3}} = \frac{1}{3} \cr & {\text{Now}},\frac{1}{3}\,{\text{work}}\,{\text{is}}\,{\text{done}}\,{\text{by}}\,{\text{A}}\,{\text{in}}\,{\text{20}}\,{\text{days}} \cr & {\text{The}}\,{\text{whole}}\,{\text{work}}\,{\text{will}}\,{\text{be}}\,{\text{done}}\,{\text{by}}\,{\text{A}}\,{\text{in}} \cr & {20 \times 3} = 60\,days \cr} $$
2. P can complete a work in 12 days working 8 hours a day. Q can complete the same work in 8 days working 10 hours a day. If both P and Q work together, working 8 hours a day, in how many days can they complete the work?
a) $$5\frac{5}{{11}}$$
b) $$5\frac{6}{{11}}$$
c) $$6\frac{5}{{11}}$$
d) $$6\frac{6}{{11}}$$
Explanation:
$$\eqalign{ & {\text{P}}\,{\text{can}}\,{\text{complete}}\,{\text{the}}\,{\text{work}} \cr & = \,\left( {12 \times 8} \right){\text{hrs}}{\text{.}} = 96\,{\text{hrs}}{\text{.}} \cr & {\text{Q}}\,{\text{can}}\,{\text{complete}}\,{\text{the}}\,{\text{work}} \cr & = \left( {8 \times 10} \right){\text{hrs}}{\text{.}} = 80\,{\text{hrs}}{\text{.}} \cr & {\text{P's}}\,{\text{1}}\,{\text{hour's}}\,{\text{work}} = \frac{1}{{96}}\,{\text{and}} \cr & {\text{Q's}}\,{\text{1}}\,{\text{hour's}}\,{\text{work}} = \frac{1}{{80}} \cr & \left( {{\text{P + Q}}} \right){\text{'s}}\,{\text{1}}\,{\text{hour's}}\,{\text{work}} \cr & = {\frac{1}{{96}} + \frac{1}{{80}}} = \frac{{11}}{{480}} \cr & {\text{So,}}\,{\text{both}}\,{\text{P}}\,{\text{and}}\,{\text{Q}}\,{\text{will}}\,{\text{finish}}\,{\text{the}}\,{\text{work}} \cr & = {\frac{{480}}{{11}}} {\text{ hrs}}{\text{.}} \cr & {\text{Number}}\,{\text{of}}\,{\text{days}}\,{\text{of}}\,{\text{8}}\,{\text{hours}}\,{\text{each}} \cr & {\frac{{480}}{{11}} \times \frac{1}{8}} = \frac{{60}}{{11}}{\text{days}} = 5\frac{5}{{11}}{\text{days}} \cr} $$
3. 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?
a) 3
b) 5
c) 7
d) Cannot be determined
Explanation:
$$\eqalign{ & 1\,woman's\,1\,day's\,work = \frac{1}{{70}} \cr & {\text{1}}\,{\text{child's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{{140}} \cr & \left( {{\text{5}}\,{\text{women + 10}}\,{\text{children}}} \right){\text{'s}}\,{\text{day's}}\,{\text{work}} \cr & = {\frac{5}{{70}} + \frac{{10}}{{140}}} = {\frac{1}{{14}} + \frac{1}{{14}}} = \frac{1}{7} \cr & {\text{5}}\,{\text{women}}\,{\text{and}}\,{\text{10}}\,{\text{chidren}}\,{\text{will}}\,{\text{complete}}\,{\text{the}}\,{\text{work}}\,{\text{in}}\,{\text{7}}\,{\text{days}} \cr} $$
4. X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?
a) 6 Days
b) 10 Days
c) 15 Days
d) 20 Days
Explanation:
$$\eqalign{ & {\text{work}}\,{\text{done}}\,{\text{by}}\,{\text{X}}\,{\text{in}}\,{\text{4}}\,{\text{days}} \cr & = {\frac{1}{{20}} \times 4} = \frac{1}{5} \cr & {\text{Remaining}}\,{\text{work}} \cr & = {1 - \frac{1}{5}} = \frac{4}{5} \cr & \left( {{\text{X + Y}}} \right){\text{'s}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} \cr & = {\frac{1}{{20}} + \frac{1}{{12}}} = \frac{8}{{60}} = \frac{2}{{15}} \cr & \frac{2}{{15}}{\text{work}}\,{\text{is}}\,{\text{done}}\,{\text{by}}\,{\text{X}}\,{\text{and}}\,{\text{Y}}\,{\text{in}}\,{\text{1}}\,{\text{day}}. \cr & \,\frac{4}{5}\,{\text{work}}\,{\text{will}}\,{\text{be}}\,{\text{done}}\,{\text{by}}\,{\text{X}}\,{\text{and}}\,{\text{Y}}\,{\text{in}} \cr & {\frac{{15}}{2} \times \frac{4}{5}} = 6\,{\text{days}} \cr & {\text{Hence,}}\,{\text{total}}\,{\text{time}}\,{\text{taken}} \cr & = \left( {6 + 4} \right)\,{\text{days}} \cr & = 10\,{\text{days}} \cr} $$
5. 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?
a) 11 days
b) 13 days
c) $$20\frac{3}{{17}}$$ days
d) None of these
Explanation:
$$\eqalign{ & {\text{Ratio}}\,{\text{of}}\,{\text{times}}\,{\text{taken}}\,{\text{by}}\,{\text{A}}\,{\text{and}}\,{\text{B}} \cr & = 100:130 = 10:13 \cr & {\text{Suppose}}\,{\text{B}}\,{\text{takes}}\,x\,{\text{days}}\,{\text{to}}\,{\text{do}}\,{\text{the}}\,{\text{work}} \cr & {\text{Then}},10:13::23:x \cr & x = {\frac{{23 \times 13}}{{10}}} \cr & x = \frac{{299}}{{10}} \cr & {\text{A's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{{23}} \cr & {\text{B's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{{10}}{{299}} \cr & \left( {{\text{A + B}}} \right){\text{'s}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} \cr & = {\frac{1}{{23}} + \frac{{10}}{{299}}} \cr & = \frac{{23}}{{299}} \cr & = \frac{1}{{13}} \cr & A\,{\text{and}}\,{\text{B}}\,{\text{together}}\,{\text{can}}\,{\text{complete}}\,{\text{the}}\,{\text{work}}\,{\text{in}}\,{\text{13}}\,{\text{days}}{\text{.}} \cr} $$
6. Ravi and Kumar are working on an assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?
a) 7 hours 30 minutes
b) 8 hours
c) 8 hours 15 minutes
d) 8 hours 25 minutes
Explanation:
$$\eqalign{ & {\text{Number}}\,{\text{of}}\,{\text{pages}}\,{\text{typed}}\,{\text{by}}\,{\text{Ravi}}\,{\text{in}}\,{\text{1}}\,{\text{hour}} = \cr & \frac{{32}}{6} = \frac{{16}}{3} \cr & {\text{Number}}\,{\text{of}}\,{\text{pages}}\,{\text{typed}}\,{\text{by}}\,{\text{Kumar}}\,{\text{in}}\,{\text{1}}\,{\text{hour}} = \cr & \frac{{40}}{5} = 8 \cr & {\text{Number}}\,{\text{of}}\,{\text{pages}}\,{\text{typed}}\,{\text{by}}\,{\text{both}}\,{\text{in}}\,{\text{1}}\,{\text{hour}} = \cr & {\frac{{16}}{3} + 8} = \frac{{40}}{3} \cr & {\text{Time}}\,{\text{taken}}\,{\text{by}}\,{\text{both}}\,{\text{to}}\,{\text{type}}\,{\text{110}}\,{\text{pages}} \cr & = {110 \times \frac{3}{{40}}} {\text{hours}} \cr & = 8\frac{1}{4}\,{\text{hours}}\,{\text{or}}\,{\text{8}}\,{\text{hours}}\,{\text{15}}\,{\text{minutes}} \cr} $$
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:
a) $$\frac{1}{{24}}$$ day
b) $$\frac{7}{{24}}$$ day
c) $$3\frac{3}{7}$$ days
d) 4 days
Explanation:
$$\eqalign{ & (A + B + C)'s\,1\,{\text{day's work}} \cr & = {\frac{1}{{24}} + \frac{1}{6} + \frac{1}{{12}}} = \frac{7}{{24}} \cr} $$
So, all the three together will complete the job in
$$ {\frac{{24}}{7}} {\text{ days}} = 3\frac{3}{7}{\text{ days}}$$
8. 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:
a) 15
b) 16
c) 18
d) 25
Explanation: 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
$$x = {\frac{{4 \times 20}}{5}} $$
x = 16 days
Tanya takes 16 days to complete the work
9. 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:
a) 4 Days
b) 6 Days
c) 8 Days
d) 12 Days
Explanation:
$$\eqalign{ & {\text{Suppose}}\,{\text{A,}}\,{\text{B}}\,{\text{and}}\,{\text{C}}\,{\text{take}} \cr & x,\,\frac{x}{2},\,\frac{x}{3}\,{\text{days}}\,{\text{respectively}}\,{\text{to}}\,{\text{finish}}\,{\text{the}}\,{\text{work}} \cr & {\text{Then}},\, {\frac{1}{x} + \frac{2}{x} + \frac{3}{x}} = \frac{1}{2} \cr & \frac{6}{x} = \frac{1}{2} \cr & x = 12 \cr & {\text{So,}}\,{\text{B}}\,{\text{takes}}\, {\frac{{12}}{2}} \cr & = 6\,{\text{days}}\,{\text{to}}\,{\text{finish}}\,{\text{the}}\,{\text{work}} \cr} $$
10. A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days B had to leave and A alone completed the remaining work. The whole work was completed in :
a) 8 days
b) 10 days
c) 12 days
d) 15 days
Explanation:
$$\eqalign{ & \left( {{\text{A + B}}} \right){\text{'s}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} \cr & = {\frac{1}{{15}} + \frac{1}{{10}}} = \frac{1}{6} \cr & {\text{Work}}\,{\text{done}}\,{\text{by}}\,{\text{A}}\,{\text{and}}\,{\text{B}}\,{\text{in}}\,{\text{2}}\,{\text{days}} \cr & = {\frac{1}{6} \times 2} = \frac{1}{3} \cr & {\text{Remaining}}\,{\text{work}} \cr & = {1 - \frac{1}{3}} = \frac{2}{3} \cr & \frac{1}{{15}}\,{\text{work}}\,{\text{is}}\,{\text{done}}\,{\text{by}}\,{\text{A}}\,{\text{in}}\,{\text{1}}\,{\text{day}} \cr & \frac{2}{3}\,{\text{work}}\,{\text{will}}\,{\text{be}}\,{\text{done}}\,{\text{by}}\,{\text{a}}\,{\text{in}} \cr & {15 \times \frac{2}{3}} = 10\,{\text{days}} \cr & {\text{Hence,}}\,{\text{the}}\,{\text{total}}\,{\text{time}}\,{\text{taken}} \cr & = {10 + 2} = 12\,{\text{days}} \cr} $$