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\ 06-Jan-2025 Surendra Prajapati Proof-7 Reader’s Sign _______________________ Date __________

C. Fill in the blanks.
1. 12 workers can build a wall in 24 days. One worker can build it in ............... .

2. If 18 pumps can empty a reservoir in 20 hours, then the time required by 45 such pumps to empty
the same reservoir is ............... hours.
3. The circumference of a circle and its diameter vary ............... with each other.
4. If the thickness of a pile of 12 cardboard sheets is 45 mm, then the thickness of a pile of 240 sheets
is ............... mm.
5. Devangi travels 50 m distance in 75 steps, then the distance travelled in 525 steps is ............... km.
D. State whether the following statements are True (T) or False (F).

1. The time of the journey is in direct variation with the speed of the train.
2. The weight of tea and its cost represent inverse variation.
x
3. If two quantities x and y vary in such a manner that is not constant and positive, then x and y are
said to be in direct variation. y
4. If 8 men can do work in 12 days, then 16 men will do the same work in 6 days.
5. If a train 400 m long is travelling at a speed of 60 km/h, then it will take 1 minute to cross a bridge
of 600 m long.
E. Solve the following problems.
1. 560 boxes can be placed in 35 cartons. How many boxes can be placed in 15 cartons?
7
2. In 16 days, the earth picks up 6.4 × 10 kg of dust from the atmosphere. How much dust will it pick
up in 20 days?
3. If the weight of 24 sheets of thick paper is 85 g, how many sheets of the same paper would weight
5.1 kg?
4. Mayank takes 21 days to complete a project while Nishank takes 28 days to complete the same project.
How much time will they take to finish it working together?
5. The speed of a train is 90 km/h which is 240 m long. How much time will it take to pass (a) a person
standing at a platform, and (b) a platform 660 m long?

6. A bowler throws a cricket ball at a speed of 120 km/h. How long does this ball take to travel a distance
of 20 metres to reach the batsman?

7. The Management and Welfare Committee of the school is planning to develop a green shade
for painting the entire school building. For this purpose, various shades are tried by mixing
containers of green paint and white paint. Case study
Mixture A B C D E F G H Case study

White paint white 3 3 4 5 2 1 5 2
Paint
Green paint Green Paint 3 4 3 2 5 6 1 4

(a) In the above mixtures, decide which is the lightest green shade among all of them.
(b) Shade B is selected to paint the interior of classes I-V. Classes VI-VIII have to be painted
with a darker shade. Which shade A or H is darker than the shade B?
(c) If one container has one litre of paint and the building requires 112 litres for paint, how
many containers of each type are required to paint the building with the darkest green
shade?

(d) If 6 painters paint the entire building in 30 days, how many painters should the contractor
employ to finish the work in 12 days?

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