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Inverse Proportion

If two quantities a and b are related to each other in such a way that an increase in b results in a proportionate decrease in a and vice versa, then a and b are said to be inversely related or in inverse proportion.
This is expressed as  (a is inversely proportional to b).

When , we can write  where k is the constant of proportionality.


Example: If 10 men can do a piece of work in 6 days, then as the number of men decreases, the number of days taken to complete the work increases.

Useful Rules

  1. If Description: 4588.png and Description: 4582.png, then Description: 4576.png
  2. If Description: 4570.pngand Description: 4564.png, then
    1. Description: 4558.png
    2. Description: 4552.png 
    3. Description: 4545.png
  3. If Description: 4538.png, then Description: 4532.png and Description: 4526.png
  4. If Description: 4520.png, then Description: 4514.png (where x is any variable or constant)

A dealer mixes tea costing ₹6.92 per kg with tea costing ₹7.77 per kg and sells the mixture at ₹8.80 per kg and earns a profit of 17.5% on his sale price. In what proportion does he mix them?
Let us first find the cost price (C.P.) of the mixture.
If S.P. is ₹ 100, profit is 17.5.
Therefore, C.P. = ₹(100 – 17.5) = ₹82.5 = ₹165/2
If S.P. is ₹8.80, C.P. is ₹(165 × 8.80)/(2 × 100) = ₹7.26
Therefore, C.P. of the mixture per kg = ₹7.26
Profit by selling 1 kg of 1st kind tea at ₹7.26 = ₹7.26 – ₹6.92 = 34 paise
Loss by selling 1 kg of 2nd kind tea at ₹7.26 = ₹7.77 – ₹7.26 = 51 paise
We have to mix the two kinds in such a ratio that the amount of profit in the first case must balance the amount of loss in the second case.
If the quantity of first kind is x and that of the second kind is y, we have 34x = 51y
Hence, the required ratio = x:y = 51:34 = 3:2.

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