Question

how many kgs. of wheat costing rs. 8 per kg must be mixed with 86 kg of rice costing rs. 6.40 per kg so that 20% gain may be obtained by belling the mixture at rs. 7.20 per kg ?

Answer 1

Sol. S.P. of 1 kg mixture = Rs. 7.20,Gain = 20%.
? C.P. of 1 kg mixture = Rs.[(100/120)*7.20]=Rs. 6.
By the rule of alligation, we have:
C_P. of 1 kg wheat of 1st kind C.P. of 1 kg wheat of 2nd kind
(800p) . (540 p)


Mean price
( 600 p)


60 200

Wheat of 1st kind: Wheat of 2nd kind = 60 : 200 = 3 : 10.
Let x kg of wheat of 1st kind be mixed with 36 kg of wheat of 2nd kind.
Then, 3 : 10 = x : 36 or lOx = 3 * 36 or x = 10.8 kg.

Answer 2

Let x kgs of wheat be required to be mixed with 86 kg of rice

Cost of the wheat = 8x

Cost of rice = 86 × 6.40 = 550.4

Total cost = 8x + 550.4

Selling price expected after 20% of profit earned = (1+20/100) × (8x+550.40) = 1.2×(8x+550.40)

Actual selling price =Rs(7.20) × (x+86)kg

7.2 (x+86) = 1.2 (8x+550.4)

7.2 x + 619.2 = 9.6x + 660.4

41.2 = 2.4x

x = 17.1 kg

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