Page 140 - Maths Skills - 8

138 Maths

(iii) p 4 2 1 10 5 (iv) p 3 5 9 1/7 6
q 20 40 80 8 16 q 7 35 27 1/3 14

3. Temperature remaining constant, the volume of the gas varies inversely as pressure. If the volume of
the gas at pressure 360 mm is 760 cm , find the volume of the gas at pressure 400 mm, assuming that the
3
temperature remains constant throughout the experiment.
4. Twenty men can reap the harvest in 25 days. How many men must be engaged to reap the harvest in
20 days?
5. A bridge can be constructed by 1800 workers in 50 days. How many more such workers should be
employed to complete the work in 30 days?
6. Thirty-five cows can clear a field by grazing in 15 days. How many cows will graze the same field in
7 days?
7. 21 pumps can empty a water tank in 36 hours. How many hours would 56 pumps take to do the
same work?
8. 350 people have a stock of food for 15 days. How long will the same stock last for 525 such people?
9. Rations worth ` 800 last for 8 days in a hostel with 25 girls. If the number of girls were 40, how many
days would the ration last?

10. 420 men had food provisions for 35 days. After 10 days, 70 men left the group. How long will the
remaining food last?
[Hint: Since 70 men left the group after 10 days, so the remaining food is sufficient for 420 men for
25 days. Then find out for how many days the food will be sufficient for (420 – 70) men.]
11. 12 men can do a work in 6 days. How many days will 18 men take to complete the same work?

12. Working 8 hours a day a person can copy a book in 15 days. How many hours per day should he work
so that he can finish the same book in 10 days?

TIME AND WORK
In the previous section, we have seen the application of direct and inverse proportion in solving time and work,
and time and distance problems. Now, we shall start solving some complex problems related to time and work,
but before that, let us have a look at some fundamental rules.
1
(i) If A (a person) can do a work in m days, then the work done by A in 1 day = ·
m
1
(ii) If A’s 1 day’s work = , then A can complete the work in m days.
m
(iii) If A can complete the work in m days and B can do it in n days, then
1
A’s 1 day’s work = of the whole work.
m

1
B’s 1 day’s work = of the whole work.
n
1 1
(A + B)’s one day’s work = of the whole work.
m n
mn
And the whole work will be completed by both of them in days.

mn