Ques 1.
A can contains a mixture of two liquids P and Q in proportion 7 : 5. When 9 litres of mixture are drawn off and the can is filled with Q, the proportion of P and Q becomes 7 : 9. How many litres of liquids P was contained in the can initially?
Solution :
==> [ 7x -7x/12] / [ 5x-5x/12 +9 ] = 7/9
==> X = 3
Initially P = 7*3 = 21 L
Ques 2.
A business man he has two qualities of gold one of 12 carats and another of 16 carats purity. In what proportion should he mix both to make an ornament of 15 carats purity?
Solution :
12 16
15
1 3
Ratio = 1 : 3
Ques 3.
Vessels P and Q contain mixture of milk and water in the ratio 4 : 5 and 5 : 1 respectively. In what ratio should quantities of mixture be taken from P and Q to form a mixture in which milk to water is in the ratio 5 : 4?
Solution :
4/9 5/6
5/9
5/18 1/9
Ratio = 5:2
Ques 4.
50 g of an alloy of Gold and Silver contains 80% Gold (be weight). The quantity of Gold , that is to be mixed up with this alloy, so that it may contain 95% Gold , is
Solution :
80 % 100%
95%
5% 15%
Ratio = 1 : 3
1 unit ------- 50
3 units ------ 150
Ques 5.
A man has 80 kg of Silver , a part of which he sells at 5% loss and the rest at the cost price. In this business he incurs a loss of 3%. Find the quantity which he sells at the cost price.
Solution :
95 100
97
3 2
Ratio = 3 : 2
5 units -------- 80
1 unit ------- 16 kg
Ques 6.
600 gm of solution has 40% Sulphur in it. How much Sulphur should be added to make it 50% in the solution?
Solution :
40% 100%
50%
50% 10%
Ratio = 5 :1
5 units -------- 600
1 unit -------- 120
Ques 7.
A is 38 times as heavy as B and C is 18 times as heavy as B. In what ratio should these metals be mixed so that the mixture may be 30 times as heavy as Y?
Solution :
38 18
30
12 8
Ratio = 3 : 2
Ques 8.
A sum of Rs. 41 was divided among 50 children. Each boy gets 90 paise and each girl 65 paise. The number of boys is
Solution :
Each student get = 8200/50 = 164
90 65
82
17 8
Ratio = 17 : 8
25 units ----------------- 50
17 units ---------------- 34 boys
Ques 9.
A container contained 160L of Apple Juice . From this container 16L of Juice was taken out and replaced by water. This process was further repeated two times. How much Juice is now contained in the container?
Solution :
Remaining Quantity = X ( 1 - (y/x))^n
X = Initial Quantity
Y = Taken out quantity
n = number of times operation performed
==> 160 (1- (16/160))^3 = 116.64
Ques 10.
In three vessels each of 20 L capacity, mixture of Sugar and water is filled, the ratios of sugar and water are 2 : 1, 3 : 1 and 3 : 2 in the three respective vessels, if all the three vessels are emptied into a single large vessel, find the proportion of sugar and water in the mixture.
Solution :
Required Ratio = ( 2/3 + 3/4 + 3/5 ) / (1/3 + 1/4 + 2/5 ) = 121 :59
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