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10. Direct and Inverse Proportions
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Q63 of 106 Page 310

If x varies inversely as y and x = 20 when y = 600, find y when x = 400.

If x varies inversely as y.


∴ xy = k(constant) …(i)


If x = 20 and y = 600


∴xy = 20× 600 = 12000


⇒ k = 12000


When x = 400, then from Eq. (i)


y× 400 = k


⇒ y × 400 = 12000


⇒


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61

Which of the following vary directly and which vary inversely with each other and which are neither of the two?

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(iii) The number of people working and the quantity of work.


(iv) Simple interest on a given sum and the rate of interest.


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62

Which of the following vary directly and which vary inversely with each other and which are neither of the two?

(i) The quantity of rice and its cost.


(ii) The height of a tree and the number of years.


(iii) Increase in cost and number of shirts that can be purchased if the budget remains the same.


(iv) Area of land and its cost.


(v) Sales Tax and the amount of the bill.

64

The variable x varies directly as y and x = 80 when y = 160, What is y when x is 64.

65

l varies directly as m and l is equal to 5, when , find l when .

Questions · 106
10. Direct and Inverse Proportions
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