1. A can do a piece of work in 20 days and B in 40 days. If they work together for 5 days, then the fraction of the work that is left is ?

a) $$\frac{5}{8}$$

b) $$\frac{8}{{15}}$$

c) $$\frac{7}{{15}}$$

d) $$\frac{1}{{10}}$$

Explanation: L.C.M of total work = 40

One day work of A = $$\frac{{40}}{{20}}$$ = 2 unit/day

One day work of B = $$\frac{{40}}{{40}}$$ = 1 unit/day

(A + B)'s one day work is (2 + 1) units

(A + B)'s 5 day work is 3 × 5 = 15 units

Work left = 40 - 15 = 25

Fraction of work left

$$\eqalign{ & = \frac{{{\text{Work left}}}}{{{\text{Total work}}}} \cr & = \frac{{25}}{{40}} \cr & = \frac{5}{8} \cr} $$

2. If there is a reduction in the number of workers in a factory in the ratio 15 : 11 and an increment in their wages in the rate 22 : 25, then the ratio by which the total wages of the workers should be decreased is =

a) 6 : 5

b) 5 : 6

c) 3 : 7

d) 3 : 5

Explanation:

Earlier | : | Now | |

No.of worker | 15 | : | 11 |

Wages | 22 | : | 25 |

Total wages | 330 | 275 | |

Total wages | 6 | : | 5 |

3. x does $$\frac{1}{4}$$ of a job in 6 days. y completes rest of the job in 12 days. Then x and y could complete the job together in = ?

a) $${\text{9 days}}$$

b) $${\text{8}}\frac{1}{8}{\text{ days}}$$

c) $${\text{9}}\frac{3}{5}{\text{ days}}$$

d) $${\text{7}}\frac{1}{3}{\text{ days}}$$

Explanation: x does $$\frac{1}{4}$$ work in 6 days.

x does complete work in 6 × 4 = 24 days

y does complete the $$\frac{3}{4}$$ work in 12 days.

y does complete work in 12 × $$\frac{4}{3}$$ = 16 days

x and y together can complete a work in

$$\eqalign{ & = \frac{{16 \times 24}}{{16 + 24}} \cr & = \frac{{48}}{5} \cr & = 9\frac{3}{5}\,{\text{days}} \cr} $$

4. Reena, Aastha and Shloka can independently complete a piece of work in 6 hours, 4 hours and 12 hours respectively. If they work together, how much time will they take to complete that piece of work ?

a) 2 hours

b) 5 hours

c) 6 hours

d) 8 hours

Explanation:

$$\eqalign{ & {\text{Reena's 1 hour's work}} = \frac{1}{6}{\text{ }} \cr & {\text{Aastha's 1 hour's work}} = \frac{1}{4}{\text{ }} \cr & {\text{Shloka's 1 hour's work}} = \frac{1}{{12}}{\text{ }} \cr} $$

( Reena + Aastha + Shloka )'s 1 hour's work

$$\eqalign{ & = \frac{1}{4} + \frac{1}{6}{\text{ + }}\frac{1}{{12}} \cr & {\text{ = }}\frac{6}{{12}} \cr & = \frac{1}{2} \cr} $$

They together take 2 hours to complete the work.

5. Amit and Sumit can plough a field in 4 days. Sumit alone can plough the field in 6 days. In how many days will Amit alone plough the feild ?

a) 10 days

b) 12 days

c) 14 days

d) 15 days

Explanation:

$$\eqalign{ & {\text{Amit's 1 day's work }} \cr & = \left( {\frac{1}{4} - \frac{1}{6}} \right) \cr & = \frac{1}{{12}} \cr} $$

Amit alone can plough the field in 12 days.

6. Working efficiencies of P and Q for completing a piece of work are in the ratio 3 : 4. The number of days to be taken by them to complete the work will be in the ratio ?

a) 3 : 2

b) 2 : 3

c) 3 : 4

d) 4 : 3

Explanation: Since we know efficiency and time are inversely proportional to each other.

$$\eqalign{ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{P}}:{\text{Q}} \cr & {\text{Efficiency }}3:4 \cr & {\text{Time }}\,\,\,\,\,\,\,\,\,\,{\text{ }}4:3 \cr} $$

7. 5 men can do a piece of work in 6 days while 10 women can do it in 5 days. In how many days can 5 women and 3 men do it ?

a) 4 days

b) 5 days

c) 6 days

d) 8 days

Explanation:

$$\eqalign{ & {\text{5M}} \times {\text{6 days}} = {\text{10W}} \times {\text{5 days}} \cr & {\text{3M}} = {\text{5W}} \cr & \frac{{\text{M}}}{{\text{W}}} = \frac{5}{3} \cr & 1{\text{M}}\left( {{\text{work}}} \right) = 5{\text{ units/day}} \cr & {\text{1W}}\left( {{\text{work}}} \right) = 3{\text{ units/day}} \cr & {\text{Total work}} \cr & = \left( {{\text{5M}} \times {\text{6}}} \right) \cr & = {\text{5}} \times {\text{5}} \times {\text{6}} \cr & = {\text{150 units}} \cr & {\text{Required time for }}\left( {{\text{5W}} + {\text{3M}}} \right) \cr & = \frac{{{\text{Total work}}}}{{{\text{Work done/day}}}} \cr & = \frac{{150}}{{\left( {5 \times 3 + 3 \times 5} \right)}} \cr & = \frac{{150}}{{30}} \cr & = 5{\text{ days}} \cr} $$

8. 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 ?

a) $${\text{9}}\frac{1}{5}{\text{ days}}$$

b) $${\text{9}}\frac{2}{5}{\text{ days}}$$

c) $${\text{9}}\frac{3}{5}{\text{ days}}$$

d) $${\text{10 days}}$$

Explanation:

$$\eqalign{ & \left( {{\text{A}} + {\text{B}} + {\text{C}}} \right){\text{'s 1 day's work}} = \frac{1}{4} \cr & {\text{A's 1 day's work}} = \frac{1}{{16}} \cr & {\text{B's 1 day's work}} = \frac{1}{{12}} \cr & {\text{C's 1 day's work}} \cr & = \frac{1}{4} - \left( {\frac{1}{{16}} + \frac{1}{{12}}} \right) \cr & = \left( {\frac{1}{4} - \frac{7}{{48}}} \right) \cr & = \frac{5}{{48}} \cr & {\text{So, C alone can do the work in }} \cr & = \frac{{48}}{5} \cr & = 9\frac{3}{5}{\text{ days}} \cr} $$

9. A can complete $$\frac{1}{3}$$ of a work in 5 days and B, $$\frac{2}{5}$$ of the work in 10 days. In how many days both A and B together can complete the work ?

a) $${\text{7}}\frac{1}{2}$$

b) $${\text{8}}\frac{4}{5}$$

c) $${\text{9}}\frac{3}{8}$$

d) 10

Explanation: Whole work will be done by A in

$$\eqalign{ & = \left( {5 \times 3} \right) \cr & = 15{\text{ days}} \cr} $$

Whole work will be done by B in

$$\eqalign{ & = \left( {10 \times \frac{5}{2}} \right) \cr & = 25{\text{ days}} \cr} $$

$$\eqalign{ & {\text{A's 1 day's work}} = \frac{1}{{15}} \cr & {\text{B's 1 day's work}} = \frac{1}{{25}} \cr & \left( {{\text{A}} + {\text{B}}} \right){\text{'s 1 day's work}} \cr & {\text{ = }}\left( {\frac{1}{{15}} + \frac{1}{{25}}} \right) \cr & = \frac{{16}}{{150}} \cr & = \frac{8}{{75}} \cr} $$

A and B together can complete the work in

$$\eqalign{ & = \frac{{75}}{8} \cr & = 9\frac{3}{8}{\text{days}}{\text{.}} \cr} $$

10. If 3 men or 6 women can do a piece of work in 16 days, in how many days can 12 men and 8 women do the same piece of work ?

a) 4 days

b) 5 days

c) 3 days

d) 2 days

Explanation:

$$\eqalign{ & {\text{3m}} \times {\text{16}} = {\text{6w}} \times {\text{16}} \cr} $$

$$\frac{{\text{m}}}{{\text{w}}} = $$ $$\frac{{2 \to {\text{Efficiency of men}}}}{{1 \to {\text{Efficiency of women}}}}$$

$$\eqalign{ & {\text{Total work}} = 3 \times 2 \times 16 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 96{\text{ units}} \cr} $$

$${\text{One day work of}}$$ $$\left( {{\text{12m}} + {\text{8w}}} \right)$$

$$\eqalign{ & = 12 \times 2 + 8 \times 1 \cr & = 32{\text{ units}} \cr} $$

$${\text{Total time taken by}}$$ $$\left( {{\text{12m}} + {\text{8w}}} \right)$$

$$\eqalign{ & = \frac{{96}}{{32}} \cr & = 3{\text{ days}} \cr} $$