Page 107 - ICSE Math 8

4. Reena can make a doll in 6 days, Meena in 10 days and Kavya in 15 days. Reena and Meena work for
3 days. How long will it take Meena and Kavya to finish the work?
1
5. Tarun can paint th of a painting in 8 days. How many days will he take to complete the painting?
4
6. 54 girls make 270 garlands in 1 hour. How many garlands will 9 girls make in 3 hours?
1 3
7. A pipe can fill th of the cistern in 16 minutes. In how many minutes, can it fill th of the cistern?
4 4
8. A cistern can be filled by a tap in 7 hours and emptied by an outlet pipe in 9 hours. How long will it take
to fill the cistern if both the tap and the pipe are opened together?
9. Two taps A and B can fill a water tank in 6 and 9 hours respectively. Another tap C empty the whole tank
in 12 hours. How long would they take to fill the tank if all the three taps are opened simultaneously?
10. Varun and Arun can plough a field in 12 hours and 18 hours respectively. Varun ploughs the field for
4 hours after that he leaves and then Arun ploughs the remaining field. How long did Arun take to plough
the remaining field?
11. A can do a certain work in 12 days, B in 18 days and C in 24 days. A and B work together for 3 days and
then A leaves. The remaining work is done by B and C. How long did B and C take to complete the work?
12. 6 pumps can irrigate a large farm in 4 days if work for 8 hours each day. How many hours each day did
5 pumps work if the same farm was irrigated in 12 days?

AT A GLANCE

¾ If x and y are two quantities and y increases with an increase in x or y decreases with a decrease in x then
x and y are in direct variation.
x x
¾ 1 = k = 2 fi x : x = y : y 2
1
2
1
y 1 y 2
¾ If x and y are two quantities and y increases with a decrease in x or y decreases with an increase in x then
x and y are in inverse variation.
¾ x y = k = x y 2 fi x : x = y : y 1
2
2
1
2
1 1
 1
¾ If a person X completes a work in n days, then the work completed by him in 1 day is   .
n

 1
¾ If a person X completes   work in 1 day, then the time taken by him to complete the work is n days.

n
¾ If a pipe fills a tank/cistern in x hours, then the part of the tank/cistern filled in 1 hour is 1 or the work
1 x
done by the inlet in 1 hour is .
x 1
¾ If a pipe empties a full tank in y hours, then the part of the tank emptied in 1 hour is or the work done
 1  y
by the outlet in 1 hour is −   y .


MENTAL MATHS

Direct and inverse variation
1. Choose the correct option.
(a) The quantity of rice sold by two shopkeepers is in the ratio 3 : 5. If the second shopkeeper sold
25 kg of rice, the quantity of rice sold by the first shopkeeper is:
(i) 18 kg (ii) 15 kg (iii) 20 kg (iv) 12 kg

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