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Mixture & Alligation  01
01.
A merchant has 1000 kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is:
1
400 kg
2
560 kg
3
600 kg
4
640 kg
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Answer:
1
Explanation:
Solution:
02.
8 litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of water is 16 : 65. How much wine did the cask hold originally?
1
18 litres
2
24 litres
3
32 litres
4
42 litres
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Answer:
1
Explanation:
Solution:
Let the quantity of the wine in the cask originally be
x
litres.
Then, quantity of wine left in cask after 4 operations
=
[
x
(
1
−
8
x
)
4
]
litres
∴
⎛
⎝
x
(
1
−
(
8
x
)
)
x
4
⎞
⎠
=
16
81
⇒
(
1
−
8
x
)
4
=
(
2
3
)
4
⇒
(
x
−
8
x
)
=
2
3
⇒
3
x
−
24
=
2
x
⇒
x
=
24
$$\begin{array}{rl}& =\left[x{\left(1\frac{8}{x}\right)}^{4}\right]\phantom{\rule{thinmathspace}{0ex}}\text{litres}\\ & \therefore \left({\frac{x\left(1\left(\frac{8}{x}\right)\right)}{x}}^{4}\right)=\frac{16}{81}\\ & \Rightarrow {\left(1\frac{8}{x}\right)}^{4}={\left(\frac{2}{3}\right)}^{4}\\ & \Rightarrow \left(\frac{x8}{x}\right)=\frac{2}{3}\\ & \Rightarrow 3x24=2x\\ & \Rightarrow x=24\end{array}$$
03.
In what ratio must a grocer mix two varieties of tea worth Rs. 60 a kg and Rs. 65 a kg so that by selling the mixture at Rs. 68.20 a kg he may gain 10%?
1
3 : 2
2
3 : 4
3
3 : 5
4
4 : 5
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Answer:
1
Explanation:
Solution:
04.
Find the ratio in which rice at Rs. 7.20 a kg be mixed with rice at Rs. 5.70 a kg to produce a mixture worth Rs. 6.30 a kg.
1
1 : 3
2
2 : 3
3
3 : 4
4
4 : 5
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Answer:
1
Explanation:
Solution:
05.
In what ratio must water be mixed with milk to gain 16 ⅔% on selling the mixture at cost price?
1
1 : 6
2
6 : 1
3
2 : 3
4
4 : 3
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Answer:
1
Explanation:
Solution:
06.
A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containing 19% alcohol and now the percentage of alcohol was found to be 26%. The quantity of whisky replaced is:
1
^{1}
/
_{3}
2
^{2}
/
_{3}
3
^{2}
/
_{5}
4
^{3}
/
_{5}
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Answer:
1
Explanation:
Solution:
07.
How many kilogram of sugar costing Rs. 9 per kg must be mixed with 27 kg of sugar costing Rs. 7 per kg so that there may be a gain of 10% by selling the mixture at Rs. 9.24 per kg?
1
36 kg
2
42 kg
3
54 kg
4
63 kg
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Answer:
1
Explanation:
Solution:
08.
A dishonest milkman professes to sell his milk at cost price but he mixes it with water and thereby gains 25%. The percentage of water in the mixture is:
1
4%
2
6
^{1}
/
_{4}
%
3
20%
4
25%
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Answer:
1
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09.
In what ratio must a grocer mix two varieties of pulses costing Rs. 15 and Rs. 20 per kg respectively so as to get a mixture worth Rs. 16.50 kg?
1
3 : 7
2
5 : 7
3
7 : 3
4
7 : 5
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Answer:
1
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Solution:
10.
A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3 : 5?
1
4 litres, 8 litres
2
6 litres, 6 litres
3
5 litres, 7 litres
4
7 litres, 5 litres
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Answer:
1
Explanation:
Solution:
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