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Q11. 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?

Given : A school has 8 periods a day each of 45 minutes duration. So, if the school hours of school is fixed then there exists an inverse relationship between each period duration and the number of periods. We can take the time of each period to be 't' if the school has 9 periods a day. Hence we can write the relation as;       or      . The time of each period would be 40 minutes when 9...

Q10. Two persons could fit new windows in a house in 3 days.

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

(ii) So, now we are calculating the number of persons that would be needed to fit the windows in one day. Let it be 'y'. So from previous part (i) we have the relation;  . or    . hence the required number of persons would be 6.

Q10.Two persons could fit new windows in a house in 3 days.

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

Here, given that 2 persons could fit new windows in a house in 3 days. (i) 1 person has fallen ill so, now the number of persons remaining is only one. Assume that the only person which is working takes the time of 'x' days. hence we could write the inverse relation as; or       . One person will take 6 days to complete that window job.

Q9. A car takes $2$ hours to reach a destination by travelling at the speed of  $\inline 60 \; km/h$ . How long will it take when the car travels at the speed of $\inline 80 \; km/h$ ?

Given that a car has a speed of 60 km/h which is travelling to a destination and takes 2 hours to complete it. Speed and time are inversely related to each other. Assume the time it would take when travelling at 80km/h be 'x' Therefore we can write the equation when the car travels at the speed of 80 km/h as: or      or

Q8. 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?

Given that a factory requires 42 machines to produce a given number of articles in 63 days. Then we know that as the number of machines increases the time taken to produce a given number of articles decreases. Hence there holds an inverse relation here, And let the number of machines required to produce the same number of articles in 54 days be 'x'. Then the relation;             or       ...

Q7. A batch of bottles were 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?

We can easily calculate the required number of boxes to be filled, let us assume it to be 'x' Given that a batch of bottles were packed in 25 boxes with 12 bottles in each box,                    Hence the total number of bottles will be . So, as they produced the same number of bottles every batch and as the number of boxes increases, the bottles in each box decrease. Hence there holds an...

Q6. A contractor estimates that $3$ persons could rewire Jasminder’s house in $4$ days. If, he uses $4$ persons instead of three, how long should they take to complete the job?

Here the situation is given that a contractor estimates that 3 persons could rewire Jasminder's house in 4 days. Now, as the number of person increases the time they take to complete the job will decrease. Hence there is an inverse relationship among the number of persons and the time they took. Jasminer now uses 4 persons instead of 3, then we can assume the time 4 persons will take be 'x' So,...

Q5. 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?

The farmer has 20 animals to feed for 6 days and after that farmer added 10 more animals to feed that counts to (20+10 = 30). So, assume that food will now long last to 'x' days. As the number of animals increases the required food increases but the day up to which the food will long last decreases. Hence there exist an inverse proportion between the number of days and the number of...

Q4. 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 $4$?

Given that the box of sweets is divided among 24 children, getting 5 sweets each. If the number of children is reduced by 4 then the number of children now is . As here if the number of children increases then the number of sweets they will get decreases hence we can say that there exists an inverse relationship between them. Hence, if we assume: Number of children before (x1)  = 24  Number of...

Q3. Rehman is making a wheel using spokes. He wants to fix equal spokes in such a way that the angles between any pair of consecutive spokes are equal. Help him by completing the following table.

(iii) How many spokes would be needed, if the angle between a pair of consecutive spokes is$40^{\circ}$ ?

 Number of spokes 4 6 8 10 12 Angle between a pair of consecutive $90^{\circ}$ $60^{\circ}$ .... .... ....

If the angle between a pair of consecutive spokes is   then, Number of spokes needed would be  Hence the required number of spokes for having 40 degrees of angle is 9.

Q3. Rehman is making a wheel using spokes. He wants to fix equal spokes in such a way that the angles between any pair of consecutive spokes are equal. Help him by completing the following table.

(ii) Calculate the angle between a pair of consecutive spokes on a wheel with 15 spokes.

 Number of spokes 4 6 8 10 12 Angle between a pair of consecutive $90^{\circ}$ $60^{\circ}$ .... .... ....

The angle between a pair of consecutive spokes on a wheel with 15 spokes is calculated as: as we know the constant value  then we can easily calculate the angle for 15 spokes:   Hence angle made is 24 degrees.

Q3. Rehman is making a wheel using spokes. He wants to fix equal spokes in such a way that the angles between any pair of consecutive spokes are equal. Help him by completing the following table.

(i) Are the number of spokes and the angles formed between the pairs of consecutive spokes in inverse proportion?

 Number of spokes 4 6 8 10 12 Angle between a pair of consecutive $90^{\circ}$ $60^{\circ}$ .... .... ....

(i) Calculating the angle formed when using a different number of spokes: The angle formed when using 8, 10, and 12 number of spokes a1,a2, and a3 respectively. Hence, we have  For 8 number of spokes: For 10 number of spokes: For 12 number of spokes: Number of spokes (x) 4 6 8 10 12 Angle between a pair of consecutive spokes (y) 90° 60° 45° 36° 30° Calculating xy: Hence we say...

Q2. 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?

 Number of winners 1 2 4 5 8 10 20 Prize for each winner (in Rs.) 1,00,000 50,000 .... .... .... .... ....

Let us assume that for the number of winners 4, 5, 8, 10 and 20 are x1, x2, x3, x4, and x5 respectively and given that the prize money of Rs. 1,00,000 is to be divided equally amongst the winners. Thus we have, For 4 number of winners: So Rs. 25,000 to be distributed among each. For 5 number of winners:   So Rs. 20,000to be distributed among each. For 8 number of winners:   So Rs. 12,500 to be...

Q1. 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 in 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.

(i) As the number of workers on a job increases the time taken to complete the job decreases, hence it is an inverse proportion. (ii) Distance and time are directly proportional to each other as time increases you could travel more distance compared to if you get less time to travel. Hence it is not an inverse proportion. (iii) Both area of cultivated land and crop arvested are directly...

Observe the below table and find which pair of variables (here x and y) are in inverse proportion.

iii)

Finding if x and y are in inverse proportion: Two quantities x and y are said to vary in inverse proportion, if there exists a relation of the type xy = k between them, k being a constant so, calculating xy for each case, we have                                                                               clearly xy is not equal to a constant value 'k', hence x and y are not inversely proportional.

Observe the given table and find which pair of variables (here x and y) are in inverse proportion.

ii)

Finding if x and y are in inverse proportion: Two quantities x and y are said to vary in inverse proportion, if there exists a relation of the type xy = k between them, k being a constant so, calculating xy for each case, we have                                                                                          , clearly xy is equal to a constant value 'k=6000', hence x and y...

Observe the following tables and find which pair of variables (here x and y) are in inverse proportion.

i)

Finding if x and y are in inverse proportion: Two quantities x and y are said to vary in inverse proportion, if there exists a relation of the type xy = k between them, k being a constant so, calculating xy for each case, we have                                                                                                       , clearly xy is not equal to a constant value 'k', hence x and y...

Q2. Principal =  Rs.1000, Rate = 8% per annum. Fill in the following table and find which type of interest (simple or compound) changes in direct proportion with time period.

Given that Principal (P) = 1000 and Rate (r) = 8% per annum(per year). Calculating the Simple Interest: Formula for the simple interest is = .  So, for 1 year:  . for 2 years: . similarly for 3 years: .   Calculating the Compound Interest : The formula for the compound interest is  . So for 1 year: . for 2 years: . similarly for 3 years: . Hence we have  In case of simple interest Simple...

Q1. Observe the below table and find if x and y are directly proportional.

Calculating   we get:                                                                           So, clearly  equals to   hence it is not equal to some constant value 'k'. We can say that x and y are not directly proportional.

Q1. Observe the given table and find if x and y are directly proportional.

If x and y are directly proportional then   must be equal to a constant value let say some  'k'. Hence we then calculating:                                                                                                                     , as you can see that all these values are not equal hence,  we can say that x and y are not directly proportional.
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