Milk and water are mixed in a vessel A in the ratio 5 : 3 and in vessel B in ratio 9 : 7 . In what ratio should quantities be taken from the two vessels so as to form a mixture in which milk and water will be in the proportion of 7 : 5
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Solution
In vessel A, milk = 5 /( 5 + 3 )= 5 / 8 of the weight of mixture
In vessel B milk = 9 /( 9 + 7) = 9 / 16 of the weight of mixture
Now, we have to form a mixture in which milk be 7 / 12 of the weight of the mixture
Now according to rule of allegation:
Required ratio = , 2 : 1
In what ratio must water be mixed with milk costing Rs. 20 per litre to obtain a mixture worth of Rs. 12 per litre?
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Solution
cost of water cost of milk
8 : 12Required Ratio = 2 : 3
In what proportion must water be mixed with milk to gain 20 % by selling it at cost price?
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Solution
Let cost price of milk be Rs 1 per liter, then S.P of mixture is also Rs 1 per liter
Now CP of mixture be = 1 – ( 20 % of Rs 1 ) = 1 – ( 20 × 1 / 100 ) = 80/ 100 = Rs 4 / 5
Required ratio = 1 : 4
A sum of Rs. 4000 is lent out in two parts, one at 8% simple interest and the other at 10% simple interest. If the annual interest is Rs. 352, the sum lent at 8% is.
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Solution
Rs. 2800
Total interest of Rs 4000 in 1 year = 352
Average rate = (352 × 100) / 4000 × 1 = 8.8%
by rule of allegation(8 – 8.8) : (10 – 8.8)
= 1.2 : 0.8
= 3 : 2
part one = (4000 × 3/5) = 2400
How many kg of Basmati rice costing Rs.42/kg should a shopkeeper mix with 25 kg of ordinary rice costing Rs.24 per kg so that he makes a profit of 25% on selling the mixture at Rs.40/kg?
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Solution
Selling price at 25% profit = 40 Rs.
Mean cost price = × 40 = 32 Rs.
Ratio of basmati rice to the ordinary rice = 32 – 24: 42 – 32
or = 8:10 = 4 : 5
so for 5 kg of ordinary rice there should be 4 kg of basmati rice
so for 25 kg of ordinary rice, quantity of basmati rice is = × 25 = 20 kg
How many litres of water should be added to a 30 litre mixture of milk and water containing milk and water in the ratio of 7 : 3 such that the resultant mixture has 40% water in it?
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Solution
Milk percentage in initial; mixture = 70%
And in final mixture = (100 – 40) = 60%
Since the milk percentage remains constant.
Let added water quantity is “x” litres.
70% of 30 litres = 60% of (30 + x) lites
35 = 30 + x
x = 5 litres.
In what ratio must a person mix three kinds of tea costing Rs.60/kg, Rs.75/kg and Rs.100 /kg so that the resultant mixture when sold at Rs.96/kg yields a profit of 20%?
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Solution
Selling price = 96 Rs.
Profit = 20%
Cost price = × 96 = 80 Rs. (mean price)
Mixture-1 Mixture-3
1 : 1
Mixture-2 Mixture-3
4 : 1
Required Ratio = 1 : 4 : 2
A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2. 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more. At the end of the two removal and replacement, what is the ratio of milk and water in the resultant mixture?
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SolutionInitial quantities : Milk Water12 8After 1st operation 12 – 6 + 10 = 16 8 – 4 = 4After 2nd operation 16 – 8 + 10 = 18 4 – 2 = 2Required ratio = 18 : 2 ⇒ 9 : 1
In what ratio must water be mixed with milk costing Rs. 12 per litre to obtain a mixture worth of Rs. 8 per litre?
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Solution
By the rule of allegation:
C.P. of 1 litre of water C.P. of 1 litre of milk
Ratio of water to milk = 4 : 8 = 1 : 2
Two vessels A and B contain milk and water mixed in the ratio 4: 3 and 2: 3. In what ratio must these mixtures be mixed to form a new mixture containing half milk and half water?
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Solution
By rule of alligation
Quantity of ratio of milk in A Quantity of ratio of milk in B
:
:
7 : 5
Required Ratio = 7 : 5