Practice Alligation and mixtures problems - quantitative aptitude Online Quiz (set-1) For All Competitive Exams
Q-1) In 80 litres mixture of milk and water the ratio of amount of milk to that of amount of water is 7 : 3. In order to make this ratio 2 : 1, how many litres of water should be added ?
(a)
(b)
(c)
(d)
Quantity of milk
= $7/10 × 80 = 56$ litres
Quantity of water
= $3/10 × 80$ = 24 litres
Let x litre water be added Then,
$56/{24 + x} = 2/1$
24 + x =28 ⇒ x = 4 litres
Q-2) Zinc and copper are in the ratio of 5 : 3 in 200 gm of an alloy. How much grams of copper be added to make the ratio as 3 : 5?
(a)
(b)
(c)
(d)
Weight of zinc
= $200 × 5/8$= 125 gram
Weight of copper
= $200 × 3/8$ = 75 gram.
Let the ratio of 125 gram zinc and x gram copper be 3 : 5
= $125/x = 3/5$
$x = {125× 5}/3 = 625/3$ gram
Addition of copper in mixture
= $625/3 - 75 = {625 - 225}/3$
= $400/3 = 133{1}/3$ gram.
Q-3) Zinc and copper are in the ratio 5 : 3 in 400 gm of an alloy. How much of copper (in grams) should be added to make the ratio 5 : 4?
(a)
(b)
(c)
(d)
In 400 gm of alloy,
Zinc = $5/8 × 400$ = 250 gm.
Copper = $3/8 × 400 = 150$ gm.
If x gm of copper be mixed, then
$250/{150 + x} = 5/4$
750 + 5x = 1000
5x = 1000 - 750 = 250
x = 50 gm.
Q-4) A can contains a mixture of two liquids A and B in the ratio 7 : 5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7 : 9. Litres of liquid A contained by the can initially was
(a)
(b)
(c)
(d)
Let A = 7x litre, B = 5x litre
In 9 litres of mixture,
A = ${7x}/{12x} × 9 = 21/4$ litres
B = ${5x}/{12x} × 9 = 15/4$ litres
In new situation,
${7x - 21/4}/{5x - 15/4 + 9} = 7/9$
${28x - 21}/{20x - 15 + 36} = 7/9$
252x - 189 = 140x + 147
112x = 336
x = 3
Initial quantity of liquid A
= 7x = 7 × 3 = 21 litres
Q-5) A barrel contains a mixture of wine and water in the ratio 3 : 1. How much fraction of the mixture must be drawn off and substituted by water so that the ratio of wine and water in the resultant mixture in the barrel becomes 1 : 1 ?
(a)
(b)
(c)
(d)
Let the barrel contain 4 litres of mixture.
Wine = 3 litres
Water = 1 litre
Let x litre mixture is taken out.
Wine in (4 - x) litres mixture
= $3/4(4 - x)$
On adding x litres water, water in mixture
= $(4 - x) × 1/4 + x = 1 - x/4 + x$
= ${4 - x +4x}/4 = {4 + 3x}/4$
$3/4(4 - x) = {4 + 3x}/4$
$3 - {3x}/4 = 1 + {3x}/4$
$2 = {6x}/4$
$x = {2 × 4}/6 = 4/3$
Required answer
= ${4/3}/4 = 1/3$
Q-6) In an alloy, the ratio of copper and zinc is 5 : 2. If 1.250 kg of zinc is mixed in 17 kg 500 g of alloy, then the ratio of copper and zinc will be
(a)
(b)
(c)
(d)
Weight of copper in 17kg 500 gm
i.e. 17500 gm of alloy
= $5/7$ × 17500 = 12500 gm
Weight of zinc = (17500 - 12500) = 5000 gm
1250 gm of zinc is mixed in alloy.
Total weight of zinc
= 1250 + 5000 = 6250 gm.
Required ratio
= 12500 : 6250 = 2 : 1
Q-7) In two alloys A and B, the ratio of zinc to tin is 5 : 2 and 3 : 4 respectively. Seven kg of the alloy A and 21 kg of the alloy B are mixed together to form a new alloy. What will be the ratio of zinc and tin in the new alloy ?
(a)
(b)
(c)
(d)
In 7 kg of alloy A,
Zinc = 5 kg, Tin = 2 kg
In 21 kg of alloy B
Zinc = ${21 × 3}/7 = 9$ kg
Tin = ${21 × 4}/7 = 12$ kg
Required ratio
= (5 + 9) : (2 + 12)
= 14 : 14 or 1 : 1
Q-8) A vessel is filled with liquid, 3 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 ?
(a)
(b)
(c)
(d)
Ratio = 4 : 1
Required quantity = $1/5$
Q-9) Two vessels A and B contain milk and water mixed in the ratio 8 : 5 and 5 : 2 respectively. The ratio in which these two mixtures be mixed to get a new mixture containing 69$3/13$% milk is:
(a)
(b)
(c)
(d)
Milk in the resulting mixture = $9/13$
= ${65 - 63}/{7 × 13} = 2/{7 × 13}$
Required ratio
= $2/{7 × 13} : 1/13$ = 2 : 7
Q-10) Two alloys are both made up of copper and tin. The ratio of copper and tin in the first alloy is 1 : 3 and in the second alloy is 2 : 5. In what ratio should the two alloys be mixed to obtain a new alloy in which the ratio of tin and copper be 8 : 3 ?
(a)
(b)
(c)
(d)
By rule of alligation
Required ratio
= $1/77 : 1/44$ = 4 7