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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...
(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.
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.
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
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       ...
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...
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,...
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...
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...
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.
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.
(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...
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...
(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...
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.
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...
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...
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...
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.
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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