1. Janardan completes $$\frac{2}{3}$$ of his work in 10 days. Time he will take to complete of the same $$\frac{3}{5}$$ work, is ?
a) 4 days
b) 8 days
c) 6 days
d) 9 days
Explanation: Janardan completes $$\frac{2}{3}$$ of work in 10 days
Janardan completes 1 of work in
$$\eqalign{ & = \frac{{10 \times 3}}{2} \cr & = 15{\text{ days}} \cr} $$
He completes $$\frac{3}{5}$$ of work in
$$\eqalign{ & = 15 \times \frac{3}{5} \cr & = 9{\text{ days}} \cr} $$
2. A can do a piece of work in 12 days while B alone can do it in 15 days. With the help of C they can finish it in 5 days. If they are paid Rs. 960 for the whole work. How much money A gets ?
a) Rs. 480
b) Rs. 240
c) Rs. 320
d) Rs. 400
Explanation: (A + B)'s 1 day work
$$\eqalign{ & = \frac{1}{{12}} + \frac{1}{{15}} \cr & = \frac{{5 + 4}}{{60}} \cr & = \frac{9}{{60}} = \frac{3}{{20}} \cr} $$
(A + B + C)'s 1 day work = $$\frac{1}{5}$$
C's 1 day work
$$\eqalign{ & = \frac{1}{5} - \frac{3}{{20}} \cr & = \frac{{4 - 3}}{{20}} \cr & = \frac{1}{{20}} \cr} $$
Ratio of their work
$$\eqalign{ & = \frac{1}{{12}}:\frac{1}{{15}}:\frac{1}{{20}} \cr & = 5:4:3 \cr} $$
$$\eqalign{ & {\text{A's}}\,{\text{share}} = \frac{5}{{12}} \times 960 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}400 \cr} $$
3. Two spinning machines A and B can together produce 300000 metres of cloth in 10 hours. If machine B alone can produce the same amount of cloth in 15 hours. Then how much cloth can machine A produce alone in 10 hours ?
a) 50000 metres
b) 100000 metres
c) 150000 metres
d) 200000 metres
Explanation: Length of cloth produced by A and B in 10 hours
$$ = 300000{\text{ metres}}$$
Length of cloth produced by B in 10 hours
$$\eqalign{ & = \left( {\frac{{300000}}{{15}} \times 10} \right) \cr & = 200000{\text{ metres}} \cr} $$
Length of cloth produced by A in 10 hours
$$\eqalign{ & = \left( {300000 - 200000} \right) \cr & = 100000{\text{ metres}} \cr} $$
4. X, Y and Z complete a work in 6 days. X or Y alone can do the same work in 16 days. In how many days Z alone can finish the same work ?
a) 12
b) 16
c) 24
d) 36
Explanation: (X + Y)'s 1 day's work
$$\eqalign{ & = \left( {\frac{1}{{16}} + \frac{1}{{16}}} \right) \cr & = \frac{2}{{16}} \cr & = \frac{1}{8} \cr} $$
Z's 1 day's work =
(X + Y + Z)'s 1 day's work - (X + Y)'s 1 day's work
$$\eqalign{ & = \frac{1}{6} - \frac{1}{8} \cr & = \frac{1}{{24}} \cr} $$
Z alone can finish the work in 24 days.
5. In two days A, B and C together can finish $$\frac{1}{2}$$ of a work and in another 2 days B and C together can finish $$\frac{3}{{10}}$$ part of the work. Then A alone can complete the whole work in ?
a) 15 days
b) 10 days
c) 12 days
d) 14 days
Explanation:
$$\eqalign{ & \frac{3}{{10}}\left( {{\text{B}} + {\text{C }}} \right) = 2{\text{ days}} \cr & \left( {{\text{B}} + {\text{C }}} \right) = 2 \times \frac{{10}}{3} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{20}}{3}{\text{ days}} \cr & \frac{1}{2}\left( {{\text{A}} + {\text{B}} + {\text{C }}} \right) = 2{\text{ days}} \cr & {\text{A}} + {\text{B}} + {\text{C}} = {\text{4 days}} \cr} $$
L.C.M of total work = 20
One day work of A + B + C = $$\frac{{20}}{4}$$ = 5 unit/day
One day work of B + C = $$\frac{{20}}{{\frac{{20}}{3}}}$$ = 3 unit/day
A = 5 - 3 = 2
A alone will complete the work
$$\eqalign{ & = \frac{{20}}{2}{\text{days}} \cr & = {\text{10 days}} \cr} $$
6. Ayesha can complete a piece of work in 16 days. Amita can complete the same piece of work in 8 days. If both of them work together in how many days can they complete the same piece of work ?
a) $${\text{4}}\frac{2}{5}{\text{ days}}$$
b) $${\text{5}}\frac{1}{3}{\text{ days}}$$
c) $${\text{6 days}}$$
d) $${\text{12 days}}$$
Explanation: Ayesha's 1 day's work $$ = \frac{1}{{16}}$$
Amita's 1 day's work $$ = \frac{1}{{8}}$$
(Ayesha + Amitha)'s 1 day's work
$$\eqalign{ & = {\frac{1}{{16}} + \frac{1}{8}} \cr & = \frac{3}{{16}} \cr} $$
Both together can complete the work in
$$\eqalign{ & = \frac{{16}}{3} \cr & = 5\frac{1}{3}{\text{ days}} \cr} $$
7. A can complete a certain work in 4 minutes, B in 5 minutes, C in 6 minutes, D in 10 minutes and E in 12 minutes. The average number of units of work completed by them per minute will be =
a) 0.16
b) 0.40
c) 0.80
d) None of above
Explanation:
$$\eqalign{ & {\text{Required average,}} \cr & = \frac{{ {\frac{1}{4} + \frac{1}{5} + \frac{1}{6} + \frac{1}{{10}} + \frac{1}{{12}}} }}{5} \cr & = {\frac{{48}}{{60}} \times \frac{1}{5}} \cr & = \frac{4}{{25}} \cr & = 0.16 \cr} $$
8. A daily-wages labourer was engaged for a certain number of days for Rs. 5750, but being absent on some of those days he paid only Rs. 5000. What were his maximum possible daily wages ?
a) Rs. 125
b) Rs. 250
c) Rs. 375
d) Rs. 500
Explanation: Maximum possible daily wage
= HCF of Rs. 5750 and Rs. 5000
= Rs. 250
9. A and B together can do a piece of work in 8 days, B and C together in 10 days, while C and A together in 6 days, if they all work together the work will be completed in ?
a) $${\text{3}}\frac{3}{4}\,{\text{days}}$$
b) $${\text{3}}\frac{3}{7}\,{\text{days}}$$
c) $${\text{5}}\frac{5}{{47}}\,{\text{days}}$$
d) $${\text{4}}\frac{4}{9}\,{\text{days}}$$
Explanation: In these type of questions, always take total work as L.C.M. of number of days
L.C.M. of Total Work = 120
One day work of A + B = $$\frac{{120}}{8}$$ = 15 unit/day
One day work of B + C = $$\frac{{120}}{10}$$ = 12 unit/day
One day work of C + A = $$\frac{{120}}{6}$$ = 20 unit/day
Total units per day = 15 + 12 + 20 = 47
Efficiency of :
$$\eqalign{ & 2\left( {{\text{A}} + {\text{B}} + {\text{C}}} \right) = 47 \cr & {\text{A}} + {\text{B}} + {\text{C}} = \frac{{47}}{2} \cr} $$
(A + B + C) will complete the whole work in
$$\eqalign{ & = \frac{{120}}{{\frac{{47}}{2}}} \cr & = \frac{{240}}{{47}} \cr & = 5\frac{5}{{47}}{\text{days}} \cr} $$
10. A and B together can complete a piece of work in 8 days, B alone can complete that work in 12 days. B alone worked for four days. After that how long will A alone takes to complete the work ?
a) 15 days
b) 18 days
c) 16 days
d) 20 days
Explanation: L.C.M. of total work = 24
One day work of A + B = $$\frac{{24}}{8}$$ = 3 unit/day
B's 1 day work = $$\frac{{24}}{12}$$ = 2 units/days
A's 1 day work = 3 - 2 = 1 units/days
4 days work of B = 4 × 2 = 8 units/days
Work left = 24 - 8 = 16 units
A will complete the remaining work in
$$\eqalign{ & = \frac{{{\text{16 units}}}}{{{\text{1 unit/day}}}} \cr & = {\text{16 days}} \cr} $$