Ex. 1. In what ratio must rice at Rs. 9.30 per kg be mixed with rice at Rs. 10.80 per kg so that the mixture be worth Rs. 10 per kg ?
Sol. By the rule of alligation, we have:
C.P. of 1 kg rice of 1st kind (in paise) C.P. of 1 kg rice of 2nd kind (in paise)
930 1080 .
. Mean pnce
(in paise)
1000
80 70
:.' Required ratio = 80 : 70 = 8 : 7.
Sol. C.P. of 1 litre of milk = Rs. (20 x 2/3) = Rs. 40/3
c.p of 1 litre of milk c.p of 1 litre of milk
0 Rs.40
3
Mean price
(Rs. 32 )
3
(40/3-32/3)=8/3 (32/3-0)=32/3
\Ratio of water and milk =8 : 32 = 8 : 32 = 1 : 4
3 3
\Quantity of water to be added to 60 litres of milk = [1/4 X 60 ]litres =15 litre
Ex. 3. In what ratio must water be mixed with milk to gain 20 % by selling the mixture at cost price?
Sol. Let C.P. of milk be Re. 1 per litre.
Then, S.P. of 1 litre of mixture = Re. 1.
Gain obtained = 20%.
\ C.P. of 1 litre of mixture = Rs.[(100/120)* 1]=Rs.5/6
By the rule of alligation, we have:
C.P. of 1 litre of water C.P. of1litre ofmilk
0 Re.1
(Re. 5/6)
(1- (5/6))= 1/6 ((5/6)-0)=5/6
\Ratio of water and milk = 1/6 : 5/6 =
Ex. 4. .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 ?
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.
Ex. 5. The milk and water in two vessels A and B are in the ratio 4 : 3 and 2: 3 respectively. In what ratio, the liquids in both the vessels be mixed to obtain a new mixture in vessel C containing half milk and half water?
Sol. Let the C.P. of milk be Re. 1 per litre
Milk in 1 litre mixture of A = 4/7litre; Milk in 1 litre mixture of B = 2/5 litre;
Milk in 1 litre mixture of C = ½ litre
C.P. of 1 litre mixture in A = Re .4/7; C.P. of 1 litre mixture in B = Re.2/5
Mean price = Re.1/2
By the rule of alligation, we have:
C.P. of 1 litre mix. in A C.P. of 1 litre mix. in B
(4/7) (2/5)
(1/2)
(1/10) (1/14)
Required ratio = 1/10 : 1/14 = 7 : 5