Chapter 14

Alligation Rule 1 Theorem: The proportion in which rice at Rs x per kg must be mixed with rice at Rs y per kg, so that the mixture be worth Rsza kg, is given by y- z-x Illustrative Example Ex.: In what proportion must rice at Rs 3.10 per kg be mixed with rice at Rs 3.60 per kg, so that the mixture be worth Rs 3.25 a kg? Soln: Detail Method: Let the required ratio be x : y. As per the question, 310x + 360y = 325(x + y) or,310x + 360y = 325x+325y % or,325;c-310x = 360y-325y or, 15.v = 35y Alligation Method: CP of 1 kg cheaper rice (310paise) £ = 35 = ? . y 15 Mean Price (325 paise) CP of 1 kg dearer rice (360 paise) Quantity of cheaper _ CP of dearer Quantity of dearer 15 Mean Price Note: Mean Price - CP of cheaper _ 360-325 _ 35 _ ; ~ 325-310 " 15 ~ .-. they must be mixed in the ratio of 7 : 3. This result can be obtained directly by applying the above theorem. Exercise In what proportion must wheat at Rs 3.20 per kg be mixed with wheat at Rs 3.70 per kg, so that the mixture be worth Rs 3.35 a kg? a)9:5 b)7:5 c)7:3 d)3:l 1 In what proportion must tea at Rs 14 per kg be mixed with tea at Rs 18 per kg, so that the mixture be worth Rs 17 a kg? a) 1:1 b) 1:3 c)2:3 d)3:l 3. In what proportion must coffee at Rs 21 per kg be mixed with coffee at Rs 28 per kg, so that the mixture be worth Rs 25 a kg? a)4:3 b)4:5 c)5:4 d)3:4 4. In what proportion must cotton at Rs 24.50 per kg be mixed with cotton at Rs 30.50 per kg, so that the mixture be worth Rs 26 a kg? a) 3:1 b) 1:3 c)3:2 d)2:3 5. In what proportion must sugar at Rs 16.60 a kg be mixed with sugar at Rs 16.45 a kg so that the mixture may be worth Rs 16.54 a kg? a) 2:1 b)2:3 c)3:2 d)4:l 6. In what proportion must tea at Rs 47.50 per kg be mixed with tea at Rs 50.50 per kg to produce a mixture worth Rs 48.50 per kg? a)2:l b) 1:2 c)4:l d)3:2 7. In what proportion must a brewer mix beer at Rs 11 a litre with bear at Rs 6 a litre, so that the mixture may be worth Rs 8 a litre? a)2:l b)l:2 c)3:2 d)2:3 8. How must a grocer mix teas at Rs 6 a kg and Rs 6.50 a kg so that the mixture may be worth Rs 6.20 a kg. a)2:3 b)3:2 6)3:1 d) 1:3 9. In what ratio should gold at Rs 15 per gm be mixed with gold at Rs 10 per gm so that the resulting mixture be worth Rs 13 pergm. a)3:2 b)3:l c) 1:1 d)2:3 10. In what ratio must a grocer mix sugar at 72 paise per kg with sugar at 48 paise per kg so that by selling the mix- 1 ture at 63 paise per kg he may gain — of his outlay? a) 1:3 b)3:l c)2:3 d)3:2 11. Sugar at Rs 15 per kg is mixed with sugar at Rs 20 per kg in the ratio 2:3. Find the price per kg of the mixture. a)Rsl8 b)Rsl6 c)Rsl7 d)Rsl9 12. A grocer buys black tea at Rs 5.25 per kg and green tea at Rs 7.50 per kg. How must he mix them so that by

Chapter 14

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