# 8th Class Mathematics Time and Work Time and Work

## Time and Work

Category : 8th Class

### Introduction

In our daily life we come across many problems which are based on time and work. The term time and work are interrelated with each other. Time and work are directly proportional to each other. The amount of work done increases with the time and the amount of work left decreases with the number of labourers or workers and time. If the number of workers increases then the time taken to complete the work will decrease. Thus the number of workers and time are inversely proportional to each other. We normally solve the problems related to the time and work using unitary method.

Important Formulae for Work Related Problems

If A can do a piece of work in 'n' number of days, then

Work done by A in 1 day $=\frac{1}{n}$.

Or conversely, if A can do the work in one day is $\frac{1}{n}$.

Then A can complete the work in $\frac{\frac{1}{1}}{n}=n$ days.

Problems Related to Pipes and Cisterns

Inlet and Outlet

A pipe connected with a tank or a cistern or a reservoir that fills it is known as an inlet.

A pipe connected with a tank or a cistern or a reservoir to empty it is known as an outlet.

Formulae

If a pipe can fill a tank in $\times$ hours, then:

1. Part filled in 1 hour $=\frac{1}{x}$
2. If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (where$\text{y}>x$), then on opening both the pipes, the net part filled in 1 hour $=\left[ \frac{1}{x}-\frac{1}{y} \right]$

 $9\times 9+7=88$ $1\times 8+1=9$ $98\times 9+6=888$ $12\times 8+2=98$ $987\times 9+5=8888$ $123\times 8+3=987$ $9876\times 9+4=88888$ $1234\times 8+4=9876$ $98765\times 9+3=888888$ $12345\times 8+5=98765$ $987654\times 9+2=8888888$ $123456\times 8+6=987654$ $9876543\times 9+1=88888888$ $1234567\times 8+7=9876543$ $98765432\times 9+0=888888888$ $12345678\times 8+8=98765432$ $123456789\times 8+9=987654321$

• This chapter is based on the concept of time and work.
• Amount of work in one day if it can be finished in 'n' days is $\frac{1}{n}$.
• Conversely if the work done in one day is $\frac{1}{n}$, then time taken to finish the work is 'n' days.
• A pipe which fills the tank is called as inlet and which empty the tank is called as outlet.
• If the taken to fill the tank is 'n' hours, then tank filled in one hours is $\frac{1}{n}$.

Robert can finish the writing of the book in 8 days while James can finish the same work in 10 days. If they work together then how long they will take to finish the same work?

(a) $10\frac{1}{2}$days

(b) $6\frac{2}{3}$days

(c) $\frac{4}{9}$days

(d) $4\frac{4}{9}$days

(e) None of these

Explanation:

Work done by Robert in one day $=\frac{1}{8}$

Work done by James in one day$=\frac{1}{10}$

Work done by both in one day $=\frac{9}{40}$

Therefore, time taken by them to finish the work $=\frac{40}{9}$

Two friends Kallis and Clerk take up the work of leveling the field. If they work separately they take the time 8 hours and 12 hours respectively to finish the work of leveling the ground. They decide to finish the work doing it alternately for one hour each and so on till it is finished. If they start work at 7 A.M., when they will finish the work?

(a) 4 P.M.

(b) 4:30 P.M.

(c) 5 P.M.

(d) 5:30 P.M.

(e) None of these

Three friends Paul, Harish and Thomas take up the work of fencing the garden in their back yard and decide to help each other in their work to finish. Paul and Harish can finish the fencing work in 10 days, while Harish and Thomas can finish the work in 15 days and Thomas and Paul can finish in 25 days. If they decide to do the work separately, in how many days will Harish finish the work?

(a) $15\frac{15}{19}$days

(b) $32\frac{8}{11}$days

(c) 25 days

(d) $40\frac{1}{12}$days

(e) None of these

P and Q can finish the work in 10 days, while Q and R can finish the same work in 18 days. If P works for 5 days and Q works for 8 days, then work is finished by R in 14 days. In how many days can R alone finish the work?

(a) 31 days

(b) 33 days

(c) 30 days

(d) 24 days

(e) None of these

Out of two workman X and Y, X is twice as good as Y to perform the work assigned to them. If X can finish the assigned work in 40 days less than Y, then in how many days they together can finish the work if they work together?

(a) $31\frac{1}{3}$days

(b) $13\frac{1}{3}$days

(c) $30\frac{1}{3}$days

(d) $24\frac{5}{6}$days

(e) None of these

Two pipes A and B can fill a tank in 16 hours and 20 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?

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

(b) $8\frac{8}{9}$hours

(c) $8\frac{17}{9}$hours

(d) $8\frac{7}{9}$hours

(e) None of these

Explanation:

Part of tank filled by A in 1 hour $=\frac{1}{6}$

Part of tank filled by B in 1 hour $=\frac{1}{20}$

Part of tank filled by $(A+B)$ in 1 hour$=\left[ \frac{1}{16}+\frac{1}{20} \right]=\frac{9}{80}$

Hence both the pipes together will fill the tank in $\frac{80}{9}$hours.

A pipe can fill a tank in 16 hours but due to a leakage at the bottom, it is filled in 24 hours. If the tank is filled to full of its capacity then how much time will it take to empty the tank?

(a) 70 hours

(b) 62 hours

(c) 45 hours

(d) 38 hours

(e) None of these

Three taps P, Q and R are connected to the tank and can fill the tank in a certain time. If P and Q can fill it in 30 min and 40 min respectively, while R can empty it in 20 min. If all the three taps are kept open successively for 1 min each, then how much time it will take to fill the tank?

(a) 345 min$\frac{3}{2}$sec

(b) 346 min$\frac{3}{2}$sec

(c) 347 min$\frac{3}{2}$sec

(d) 345 min$\frac{3}{2}$sec

(e) None of these

Three people M, N, and O together earn Rs. 300 per day, while M and N earn Rs. 180 and M and O together earn Rs. 150 per day. The earning of M per day is:

(a) Rs. 60

(b) Rs. 80

(c) Rs. 90

(d) Rs. 100

(e) None of these