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(i) One of the people fell ill before the work started. How long would the job take now?

(ii) How many persons would be needed to fit the windows in one day?

Answer :

We can see that on increasing the number of persons, less time will be required to complete a job.Thus, the quantities are in inverse proportion.

(i) Let the required number of days be x.

∴\(x_1y_1 = x_2y_2\)

\(\Rightarrow 2 \times 3 = 1 \times x\)

\(\Rightarrow x = 6\)

Hence, the required number of days = 6 days

(ii) Let the required number of persons be y.

∴\(x_1y_1 = x_2y_2\)

\(\Rightarrow 2 \times 3 = y \times 1\)

\(\Rightarrow y = 6\)

Hence, the required number of persons = 6.

- 1.Which of the following are in inverse proportion? (i) The number of workers on a job and the time to complete the job. (ii) The time taken for a journey and the distance travelled at a uniform speed. (iii) Area of cultivated land and the crop harvested. (iv) The time taken for a fixed journey and the speed of the vehicle. (v) The population of a country and the area of land per person.
- 2.In a Television game show, the prize money of ₹ 1,00,000 is to be divided equally amongst the winners. Complete the following table and find whether the prize money given to an individual winner is directly or inversely proportional to the number of winners?
- 3.Rehman is making a wheel using spokes. He wants to fix equal spokes in such a way that the angles between any pair of consective spokes are equal. Help him by completing the following table. (i) Are the number of spokes and the angle formed between the pairs of consecutive spokes in inverse proportion. (ii) Calculate the angle between a pair of consecutive spokes on a wheel with 15 spokes. (iii) How many spokes would be needed, if the angle between a pair of consecutive spokes is \(40^o\)?
- 4.If a box of sweets is divided among 24 children, they will get 5 sweets each. How many would each get, if the number of the children is reduced by 4?
- 5.A farmer has enough food to feed 20 animals in his cattle for 6 days. How long would the food last if there were 10 more animals in his cattle?
- 6.A contractor estimates that 3 persons could rewire Jasminderâ€™s house in 4 days. If, he uses 4 persons instead of three, how long should they take to complete the job?
- 7.A batch of bottles was packed in 25 boxes with 12 bottles in each box. If the same batch is packed using 20 bottles in each box, how many boxes would be filled?
- 8.A factory requires 42 machines to produce a given number of articles in 63 days. How many machines would be required to produce the same number of articles in 54 days?
- 9.A car takes 2 hours to reach a destination by traveling at a speed of 60 km/h. How long will it take when the car travels at the speed of 80 km/h?
- 11.A school has 8 periods a day each of 45 minutes duration. How long would each period be, if the school has 9 periods a day, assuming the number of school hours to be the same?

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