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A vessel is filled with liquid, 4 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?
Answer – B.1/10 Explanation : Suppose the vessel initially contains 9litres of liquid.
Let x litres of this liquid be replaced with water. (4(4x/9) +x) = (5(5x/9)) X = 9/10
So, part of the mixture replaced = 9/10 * 1/9 = 1/10 Shortcut: 4:5—>9
1:1—>2
8:10
9:9
1/10
Rice worth Rs. 126 per kg and Rs. 134 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 177 per kg, the price of the third variety per kg will be:
Answer – C.224 Explanation : 126*1+134*1+2x=177*4 260+2x=708 2x==708260=448 x=448/2 = 224
One quantity of rice priced at Rs 9.30 per Kg is mixed with another quality at a certain rate in the ratio 8:7. If the mixture so formed be worth Rs 10 per Kg, what is the rate per Kg of the second quality of wheat?
Answer – B.10.80 Explanation : Let the rate of second quality be Rs x per Kg. 9.30…..…………x …………10………….
8………………………7
7X – 70 = 5.6
X = 10.80
How many kgs of rice of variety1 costing Rs.42/kg should a shopkeeper mix with 25 kgs of rice of variety2 costing Rs.24 per kg so that he makes a profit of 25% on selling the mixture at Rs.40/kg?
Answer – B.20 Explanation : 25% profit by selling the mixture at Rs.40/kg, his cost per kg of the mixture = Rs.32/kg. (x×42)+(25×24)=32(x+25) 42x+600=32x+800 10x=200 x=20kgs.
Shortcut: 125 = 40
100 = 32
42……………….24
………32…………..
8…………………….10
10 = 25
8 = 20
An alloy contains Brass, Iron and Zinc in the ratio 2:3:1 and another contains Iron, zinc and lead in the ratio 5:4:3.If equal weights of both alloys are melted together to form a third alloy, then what will be the weight of lead per kg in new alloy?
Answer – D.1/8 Explanation : Shortcut: In the first alloy, 2:3:1 =6*2
5:4:3 =12
Multiply 2 to make it equal, 4:6:2
5:4:3
Adding all, 4:11:6:3=24
3/24=1/8
A can contains 50 litres of milk. 10 litres of this milk is taken out and replaced with water. This process is repeated twice. Find the amount of remaining milk in the mixture?
Answer – D.128/5litres Explanation : Remaining milk = 50 [1 – (10/50)] = 128/5
A milkman mixes 6 litres of free tap water with 20litres of pure milk. If the cost of pure milk is Rs.28 per litre the % Profit of the milkman when he sells all the mixture at the cost price is
Answer – C. 30% Explanation : Profit=28*6=728 Cp=28*20=560 Profit = 168*100/560=30%
Rs 4000 is lent in 2 parts, 1 part at 8% per annum and 2nd part at 12% per annum. At the end of a year Rs 400 is received as simple interest. Find the part lent at 8% p.a.
Answer – C.2000 Explanation : Effective interest rate = 400/4000*100 = 10 8…………………12
……… 10………..
2…………………..2
1:1
1/2*4000 = 2000
A 144 litres of mixture contains milk and water in the ratio 5 : 7. How much milk need to be added to this mixture so that the new ratio is 23 : 21 respectively?
Answer – D.32 litres Explanation : 144 == 5:7
60 : 84
Now == 21 = 84 23 = 92
9260 = 32
In a 100 litre mixture of milk and water, the % of water is only 20%. The milkman gave 25 litres of this mixture to a customer and then added 25 litres of water to the remaining mixture. What is the % of milk in the final mixture?
Answer – C.60% Explanation : 80: 20 == 4:1
25 == 20:5
60 : 15
60 : 15+25 == 60:40
60%
Two vessels A and B contain a mixture of Milk and Water. In the first vessel (i.e) Vessel A has the ratio of Milk to water is 8 : 3 and in the second vessel, Vessel B has the ratio of 5 : 1. A 35 litre capacity vessel is filled from these two vessels so as to contain a mixture of Milk and water in ratio of 4 : 1. Then how many litres should be taken from the first vessel, Vessel “A”.
Answer – D. 11 L Explanation : [8/11(x) + 5/6(35x)]/[3/11(x) + 1/6(35x)] = 4/1 x = 11
When one litre of water is added to a mixture of milk and water, the new mixture contains 25% of milk. When one litre of milk is added to the new mixture, then the resulting mixture contains 40% milk. What is the percentage of milk in the original mixture?
Answer – C. 100/3 % Explanation : Original Mixture = x L In (x + 1) Mixture, quantity of milk = (x + 1)* (25/100) = (x + 1)/4 one litre of milk is added to the new mixture [((x + 1)/4 )+ 1 ]/ x + 2 = 40% x = 3 ; quantity of milk = (3 + 1)/4 = 1L percentage of milk in the original mixture = 1/3 * 100 = 100/3 %
The price of a box and a pen is Rs.60. The box was sold at a 40% profit and the pen at a loss of 10%. If the Shop keeper gains Rs.4 in the whole transaction, then how much is the cost price of Box?
Answer – C. Rs.20 Explanation : 40x/100 – 10(60x)/100 = 4 40x + 10x = 400 + 600 x = 20
A vessel contains a mixture of diesel and petrol in which there is 20% diesel.Five litres are drawn off and then the vessel is filled with petrol. If the diesel present in the mixture is now 15% then how much does the vessel hold?
Answer – B. 20 L Explanation : 20/15 = x/x5 x = 20
In a lab, two chemical solutions Acid “A” with 90% purity and Acid “B” with 96% purity are mixed resulting in 24 litres of mixture of 92% purity. How much is the quantity of the first solution, Acid “A” in the resulting mixture?
Answer – C. 16 L Explanation : 90x + (24 – x)* 96 = 24 * 92 x = 16
60 kg of a certain variety of Sugar at Rs.32 per kg is mixed with 48 kg of another variety of sugar and the mixture is sold at the average price of Rs.28 per kg. If there be no profit or no loss due to the new selling price, then what is the price of second variety of Sugar?
Answer – B. Rs.23 Explanation : Total CP of first variety = 60 * 32 = 1920 Total CP of second variety = 48 * x = 48x SP of Mixture = 1920 + (108 * 28) = 3024 1920 + 48x = 3024 => x = 23
Six litre of milk was taken out from a vessel and is then filled with water. This operation is performed two more times. The ratio of the quantity of milk now left in vessel to that of the water is 8 : 27. How much is the quantity of the milk contained by the vessel originally?
Answer – A. 18 litre Explanation : [x(16/x)/x]³ = (8/27) [x(16/x)/x]³ = (2/3)³ (x6)/x = 2/3 x = 18
A vessel is filled with 120 litres of Chemical solution, Acid “A”. Some quantity of Acid “A” was taken out and replaced with 23 litres of Acid “B” in such a way that the resultant ratio of the quantity of Acid “A” to Acid “B” is 4:1. Again 23 litres of the mixture was taken out and replaced with 28 litre of Acid “B”. What is the ratio of the Acid “A” to Acid “B” in the resultant mixture?
Answer – D. 46 : 29 Explanation : In 23 litre mixture, Quantity of Acid “B” = 23 * 1/5 = 4.6 litre Acid “A” in the mixture = 23 – 4.6 = 18.4 litre 120 – x / 23 = 4 / 1 x = 28 Ratio = 9218.4 : 18.4 + 28 Ratio = 46 : 29
18 litres of Petrol was added to a vessel containing 80 litres of Kerosene. 49 litres of the resultant mixture was taken out and some more quantity of petrol and kerosene was added to the vessel in the ratio 2:1. If the respective ratio of kerosene and petrol in the vessel was 4:1, what was the quantity of kerosene added in the vessel?
Answer – E. None of the Above Explanation : Total quantity of the mixture = 18+80 = 98 litre quantity of petrol remaining = 18/2 = 9 quantity of kerosene remaining = 80/2 = 40 (40 + 2x) / (9 + x) = 4 / 1 x = 2 Quantity of kerosene added in the vessel = 2x = 4 litre
A vessel which contains a mixture of acid and water in ratio 13:4. 25.5 litres of mixture is taken out from the vessel and 2.5 litres of pure water and 5 litres of acid is added to the mixture. If resultant mixture contains 25% water, what was the initial quantity of mixture in the vessel before the replacement in litres?
Answer – B. 68 litre Explanation : Quantity of Acid = 13x Quantity of water = 4x Total = 17x Resultant Mixture = 17x – 25.5 + 2.5 + 5 = 17x – 18 Resultant water = 4x – 25.5 * (4/17) + 2.5 = 4x – 3.5 Resultant mixture contains 25% water (17x – 18)*25/100 = 4x – 3.5 x = 4 Initial quantity = 17*4 = 68
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