Practice MCQ Questions and Answer on Alligation

31.

Wheat worth Rs. 80 per kg and Rs. 50 per kg is mixed with a third variety in the ratio 1 : 2 : 3. If the mixture is worth Rs. 75 per kg, then the price of the third variety per kg will be equal to:

(A) Rs. 95
(B) Rs. 85
(C) Rs. 80
(D) Rs. 90

Solution: $\begin{aligned} Let third variety = x \\ 80 : 50 : x \\ 1 : 2 : 3 \\ \overset{―}{80 + 100 + 3 x} = (3 + 2 + 1) \times 75 \\ 180 + 3 x = 6 \times 75 \\ 3 x = 270 \\ x = 90 per kg \end{aligned}$

32.

A vessel contained a solution of acid and water, in which water was 64%. Four litres of the solution was taken out of the vessel and the same quantity of water was added. If the resulting solution contains 30% acid, the quantity (in litres) of the water in the solution, at the beginning in the vessel, was:

(A) 8.64
(B) 15.36
(C) 12.64
(D) 11.36

Solution: $\begin{matrix} Acid & Water \\ Old \to & 36 % & 64 % \\ New \to & 30 % & 70 % \end{matrix}$ $\begin{aligned} Old mixture = Remaining + Taken out \\ = 20 L + 4 L \\ = 24 L \\ Water = 24 \times \frac{64}{100} \Rightarrow 15.36 L \end{aligned}$

33.

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?

(A) 18 litres
(B) 24 litres
(C) 32 litres
(D) 42 litres

Solution: Let the quantity of the wine in the cask originally be x litres. Then, quantity of wine left in cask after 4 operations $\begin{aligned} = [x {(1 - \frac{8}{x})}^{4}] litres \\ ∴ ({\frac{x (1 - (\frac{8}{x}))}{x}}^{4}) = \frac{16}{81} \\ \Rightarrow {(1 - \frac{8}{x})}^{4} = {(\frac{2}{3})}^{4} \\ \Rightarrow \frac{x - 8}{x} = \frac{2}{3} \\ \Rightarrow 3 x - 24 = 2 x \\ \Rightarrow x = 24 litres \end{aligned}$

34.

The ratio of milk and water in mixture of four containers are 5 : 3, 2 : 1, 3 : 2 and 7 : 4 respectively. In which container is the quantity of milk, relative to water, minimum ?

(A) First
(B) Second
(C) Third
(D) Forth

Solution: ∴According to the question,Container : $\begin{aligned} I II III IV \\ M : W M : W M : W M : W \\ 5 : 3 2 : 1 3 : 2 7 : 4 \end{aligned}$ $\begin{aligned} C o n t a i n e r (I) : \\ \frac{Milk}{Water} = \frac{5}{3} = 1.67 \\ C o n t a i n e r (II) : \\ \frac{Milk}{Water} = \frac{2}{1} = 2 \\ C o n t a i n e r (III) : \\ \frac{Milk}{Water} = \frac{3}{2} = 1.5 \\ C o n t a i n e r (IV) : \\ \frac{Milk}{Water} = \frac{7}{4} = 1.75 \end{aligned}$ ∴ The quantity of milk relative to water minimum in container third.

35.

A and B are solutions of acid and water. The ratios of water and acid in A and B are 4 : 5 and 1 : 2 respectively. If x litres of A is mixed with y litres of B, then ratio of water and acid in the mixture becomes 8 : 13. What is x : y?

(A) 5 : 6
(B) 2 : 5
(C) 3 : 4
(D) 2 : 3

Solution: In A, water = $\frac{4}{9}$ In B, water = $\frac{1}{3}$ In C, water = $\frac{8}{21}$ x : y = 3 : 4

36.

In what ratio must 45% grape juice be mixed with that of 25% grape juice so as to get a mixture of 40% grape juice?

(A) 4 : 1
(B) 3 : 1
(C) 4 : 3
(D) 2 : 3

37.

Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be:

(A) Rs. 169.50
(B) Rs. 170
(C) Rs. 175.50
(D) Rs. 180

Solution: Since first and second varieties are mixed in equal proportions. So, their average price $\begin{aligned} = Rs . (\frac{126 + 135}{2}) \\ = Rs . 130.50 \end{aligned}$ So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x. By the rule of alligation, we have: $\begin{aligned} ∴ \frac{x - 153}{22.50} = 1 \\ \Rightarrow x - 153 = 22.50 \\ \Rightarrow x = 175.50 \end{aligned}$

38.

A lump of two metals weighing 18 g is worth Rs. 87 but if their weight is interchanged, it would be worth Rs. 78.60. If the price of one metal be Rs. 6.70 per gram, find the weight of the other metal in the mixture.

(A) 8g
(B) 12g
(C) 15g
(D) 18g

Solution: Cost of (18g of 1st metal + 18g of 2nd metal) = Rs. 165.60 Cost of (1g of 1st metal + 1g metal of 2nd metal) = Rs. 9.20 Hence cost of 1g of 2nd metal, = 9.20 - 6.70 = Rs. 2.5 Mean price = Rs. $\frac{87}{18}$ Now, $\frac{quantity of 1^{st} metal}{quantity of 2^{nd} metal}$ $=$ $\frac{14}{6} : \frac{56}{30} = 5 : 4$ Quantity of 2nd metal = $\frac{18 \times 4}{9}$ = 8g

39.

A container contains 40 litres of milk. From this container 4 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?

(A) 26.34 litres
(B) 27.36 litres
(C) 28 litres
(D) 29.16 litres

Solution: $\begin{aligned} Amount of milk left after 3 operations \\ = [40 {(1 - \frac{4}{40})}^{3}] litres \\ = (40 \times \frac{9}{10} \times \frac{9}{10} \times \frac{9}{10}) litres \\ = 29.16 litres \end{aligned}$

40.

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%

Solution: Percentage of sugar in 4 litres mixture. $\begin{aligned} = \frac{9}{5 \times 4} \times 100 \\ = 45 % \end{aligned}$

«
1
2
3
4
5
6
7
8
9
10
Next ›
Last »

Indian Polity Mcq IAS GK Question India GK World GK GK questions GK Quiz Biology GK Science GK Physics GK Chemistry GK General Awareness Computer GK Political GK Indian Political GK Economics GK History GK Sports GK Geography GK Teaching Aptitude GK CTET/TET GK B Ed Entrance GK Banking GK SSC GK UPSC GK Indian Army GK Hindi Grammar GK Hindi Grammar MCQ Reasoning questions Bihar GK Rajasthan GK Jharkhand GK MP GK UP GK Chhattisgarh GK Haryana GK HP GK Maharashtra GK Electronics GK Agriculture GK States/Capitals GK Books Name & Author Arthimetic Verbal Reasoning Non Verbal Reasoning English

Practice MCQ Questions and Answer on Alligation

General Knowledge