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41. A vessel contains 60 litre of milk. 12 litres of milk taken out from it and replaced with water. Then again from mixture, 12 litres is taken out and replaced with water. The ratio of milk and water in the resultant mixture is ?

A. 16 : 9

B. 15 : 10

C. 16 : 10

D. 9 : 5

Discuss

Solution:

Total milk = 60 litres
Drawn off = 12 litres

\frac{Final quantity}{Initial quantity}

= {(1 - \frac{x}{c})}^{t}

X = Replaced quantity
C = Capacity
T = Number of process

\begin{aligned} \frac{Final quantity}{Initial quantity} = {(1 - \frac{12}{60})}^{2} \\ = {(\frac{4}{5})}^{2} \\ = \frac{16}{25} \end{aligned}

Ratio of milk and water in the resultant mixture :
= 16 : 9

42. 40 litres of a mixture of milk and water contains 10% of water, the water to be added, to make the water content 20% in the new mixture. Find how many litres water will be added ?

A. 6 litres

B. 6.5 litres

C. 5.5 litres

D. 5 litres

Discuss

Solution:

Water content in 40 litres of mixture.

\begin{aligned} = 40 \times \frac{10}{100} \\ = 4 litres \end{aligned}

∴ Milk in the mixture.

\begin{aligned} =  40 - 4 \\ = 36 litres \end{aligned}

Let x litres of water is mixed

\begin{aligned} \Rightarrow \frac{4 + x}{40 + x} = \frac{20}{100} \\ \Rightarrow x = 5 litres \end{aligned}

43. In 2 kg mixture of copper and aluminium, 30% is copper. How much aluminium powder should be added to the mixture so that the quantity of copper becomes 20% ?

A. 900 gms

B. 800 gms

C. 1000 gms

D. 1200 gms

Discuss

Solution:

According to the question,
Mixture of copper and aluminium = 2000 gms
30% is copper means
=

\frac{30}{100}

× 2000
= 600 gms copper

\begin{aligned} \Rightarrow \frac{600}{1400 + x} = \frac{20 %}{80 %} \\ \Rightarrow 1400 + x = 2400 \end{aligned}

⇒ x = 1000 gms

44. A sugar solution of 3 litres contain 60% sugar. One litre of water is added to this solution. Then the percentage of sugar in the new solution is :-

A. 30%

B. 45%

C. 50%

D. 60%

Discuss

Solution:

Percentage of sugar in 4 litres mixture.

\begin{aligned} = \frac{9}{5 \times 4} \times 100 \\ = 45 % \end{aligned}

45. Two types of tea costing Rs. 180/kg and Rs. 280/kg. In what ratio should these be mixed so that obtained mixture sold at Rs. 320/kg to earn a profit of 20% is ?

A. 3 : 13

B. 4 : 13

C. 1 : 13

D. 2 : 13

Discuss

Solution:

According to the question,
Selling price of the mixture = Rs. 320, Gain = 20%
∴ Cost price of the mixture

\begin{aligned} = 320 \times \frac{100}{120} \\ = Rs . \frac{800}{3} \end{aligned}

Now using alligation method
Alligation mcq solution image

\begin{aligned} Ratio of quantity \\ \to 40 : 260 \\ 2 : 13 \end{aligned}

46. 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. $\frac{1}{4}$

B. $\frac{1}{3}$

C. $\frac{2}{3}$

D. $\frac{1}{2}$

Discuss

Solution:

Let the quantity of liquid drawn out = x

\begin{aligned} \Rightarrow \frac{3 - \frac{3}{4} x}{1 - \frac{1}{4} x + x} = \frac{1}{1} \\ \Rightarrow 12 - 3 x = 4 - x + 4 x \\ \Rightarrow 8 = 6 x \\ \Rightarrow x = \frac{4}{3} \end{aligned}

Hence, required part of quantity

\begin{aligned} = \frac{\frac{4}{3}}{4} \\ = \frac{1}{3} \end{aligned}

47. A and B are two alloys of gold and copper prepared by mixing metals in the ratio 5 : 3 and 5 : 11 respectively. Equal quantities of these alloys are melted to form a third alloys C. The ratio of gold and copper in the alloy C is -

A. 25 : 13

B. 33 : 15

C. 15 : 17

D. 17 : 15

Discuss

Solution:

According to the question,

\begin{matrix} Alloy A \to 5 \times_{2} : 3 \times_{2} = 8 \times_{2} \\ Alloy B \to 5 : 11 = 16 \end{matrix}]

Equal quantity are mixed

\begin{aligned} Alloy A \to 10 : 6 = 16 \\ Alloy B \to 5 : 11 = 16 \\ Alloy C \to 15 : 17 \end{aligned}

48. Two blends of a commodity costing Rs. 35 and Rs. 40 per kg respectively are mixed in the ratio 2 : 3 by weight. If one-fifth of the mixture is sold at Rs. 46 per kg and the remaining at the rate Rs. 55 per kg, the profit percent is -

A. 50%

B. 20%

C. 40%

D. 30%

Discuss

Solution:

Let first blend is 2 kg and second blend is 3 kg.

\begin{aligned} Total cost price \\ = (35 \times 2) + (40 \times 3) \\ = 70 + 120 \\ = Rs . 190 \\ Total selling price \\ = (1 \times 46) + (4 \times 55) \\ = 266 [\frac{1}{5} of 5kg  =  1kg] \\ ∴ Profit percent \\ \Rightarrow \frac{Total profit}{Total cost price} \times 100 \\ \Rightarrow \frac{(266 - 190)}{190} \times 100 \\ \Rightarrow \frac{76}{190} \times 100 \\ \Rightarrow 40 % \end{aligned}

49. 12500 students appeared in an exam. 50% of the boys and 70% of the girls cleared the examination. If the total percent of student qualifying is 60% , how many girls appeared in the exam ?

A. 6500

B. 6200

C. 5500

D. 6250

Discuss

Solution:

\begin{aligned} Number of girls \\ = \frac{1}{2} \times 12500 \\ = 6250 \end{aligned}

50. 60 kg of an alloy A is mixed with 100 kg of alloy B. If alloy A has lead and tin in the ratio 3 : 2 and alloy B has tin and copper in the ratio 1 : 4, the amount of tin in the new alloy is -

A. 44 kg

B. 53 kg

C. 80 kg

D. 24 kg

Discuss

Solution:

Quantity of tin in 60 kg of A

\begin{aligned} = (60 \times \frac{2}{5}) kg \\ = 24 kg \end{aligned}

Quantity of tin in 100 kg of B

\begin{aligned} = (100 \times \frac{1}{5}) kg \\ = 20 kg \end{aligned}

∴ Quantity of tin in the new alloy
= (24 + 20) kg
= 44 kg

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