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1. A mixture of 160 gallons of wine and water contains
25% water. How much water must be added to the mixture in order to increase the percentage of water
to 40% of the new mixture?

Correct Answers :

[A]

Explanation :

There are multiple ways of solving this question. In
160 gallons since we have 25% water, the composition would be 120 gallons of wine and 40 gallons
of water. After adding more water to this, the water would become 40 + w, while the wine would remain
at 120 gallons. This 120 gallons of wine would correspond to 60% wine in the final mixture. Since, 120
= 60%, 200 = 100%. So we need to add, 40 gallons of water.

Alternately, you can solve this using options
to check, the case when the wine to water becomes 60% to 40%. In 120 gallons of wine + 40 gallons of
water, if you add 40 gallons of water, you will end up with 60% wine and 40% water. Hence, option (a)
is correct.

2. 800 students took the CAT exam in Delhi. 50% of
the boys and 90% of the girls cleared the cut off in the examination. If the total percentage of qualifying
students is 60%, how many girls appeared in the examination?

Correct Answers :

[D]

Explanation :

The ratio of boys and girls appearing for the exam
can be seen to be 3:1 using the following alligation figure.

This means that out of 800 students, there must have
been 200 girls who appeared in the exam..

3. If 10 kg of sugar costing Rs.15/kg and 20 kg of salt
costing Rs.10/kg are mixed, find the average cost ofthe mixture in Rs. per kilogram.

Correct Answers :

[A]

Explanation :

Solving the following alligation figure.

4. The average salary per head of all workers (Grade
A and Grade B) of a company is Rs. 400. The average salary of 100 grade A workers is Rs. 1000. If the average salary per head of the rest of the Grade B workers is Rs. 300, find the total number of workers in the company.

Correct Answers :

[D]

Explanation :

From the figure we can see that the ratio of Grade
A and Grade B workers is 1: 6. Since, there are 100 grade A workers, there would be 600 Grade B
workers. Hence, total number of grade B workers = 600.Total workers in the company = 100 + 600 = 700.

5. Ashok purchased two qualities of grains at the rate
of Rs. 100 per quintal and Rs. 160 per quintal. In 50 quintals of the second quality, how much grain of
the first quality should be mixed so that by selling the resulting mixture at Rs. 195 per quintal, he gains
a profit of 30%?

Correct Answers :

[A]

Explanation :

By selling at 195 if we need to get a profit of 30% it
means that the cost price would be 195/1.30 = 150.

From the alligation figure, you can see that the ratio of the quantities of the two pulses would be 1:5.
Since, we have 50 quintals of the second quality, we must have 10 quintals of the first. Hence, option (a)
is correct.

6. Two types of milk having the rates of Rs.8/kg and
Rs.10/kg respectively are mixed in order to produce a mixture having the rate of Rs.9.20/kg. What should be
the amount of the second type of milk if the amount of the first type of milk in the mixture is 20 kg?

Correct Answers :

[B]

Explanation :

Mixing Rs. 8/kg and Rs. 10/kg to get Rs. 9.20 per kg we get that the ratio of mixing is (10 – 9.2): (9.2 – 8) = 2:3. If the first milk is 20 kg, the second would be 30 kg.

7. How many kilograms of salt worth Rs. 360 per kg
should be mixed with 10 kg of salt worth Rs.420 per kg, such that by selling the mixture at Rs. 480 per kg,
there may be a gain of 20%?

Correct Answers :

[A]

Explanation :

Since by selling at Rs. 480 we want a profit of 20%, it means that the average cost required is Rs. 400 per kg. Mixing salt worth Rs. 360/kg and Rs. 420/kg to get Rs. 400/kg means a mixture ratio of 1:2. Thus, to 10 kg of the second variety we need to add 5 kg of the first variety to get the required cost price.

8. Kiran lends ` 1000 on simple interest to Harsh for
a period of 5 years. She lends a part of the amount at 2% interest and the rest at 8% and receives ` 300
as the amount of interest. How much money (in Rs.)did she lend on 2% interest rate?

Correct Answers :

[A]

Explanation :

Since Kiran earns Rs. 300 in 5 years, it means that
she earns an interest of 300/5 = Rs. 60 per year. On an investment of 1000, an annual interest of 60 represents
an average interest rate of 6%. Then using the alligation figure below:

We get the ratio of investments as 1:2. Hence, she lent one third of the amount i.e. 1 x 1000/3 = 333.33
at 2% per annum.

9. A tank contains 500 liters of wine. 50 liters of wine
is taken out of it and replaced by water. The process is repeated again. Find the proportion of water and
wine in the resulting mixture.

Correct Answers :

[C]

Explanation :

Amount of wine left = 500 x 9/10 x 9/10 = 405 liters. Hence, water = 95 liters. Ratio of water and wine = 19:81. Option (c) is correct.

10. A man purchased a table and a chair for Rs.2000. He
sold the table at a profit of 20% and the chair at a profit of 40%. In this way, his total profit was 25%.
Find the cost price (in Rs.) of the table.

Correct Answers :

[A]

Explanation :

The ratio of the cost of the table and the chair would be (40 – 25):(25 – 20) or 3:1 as can be seen from the following alligation figure: Thus, the cost of the table would be Rs.1500.

11. A dishonest shopkeeper purchased milk at Rs.100 per
litre and mixed 10 liters of water in it. By selling the mixture at the rate of Rs. 100 per litre he earns
a profit of 25%. The quantity of the amount of the mixture that he had was:

Correct Answers :

[A]

Explanation :

Cost price of the mixture = Rs. 80 per liter

Since, water = 10 liters, Pure milk = 40 liters, Total quantity of the mixture = 40+ 10 = 50 liters.

12. A tank has a capacity of 10 gallons and is full of
alcohol. 2 gallons of alcohol are drawn out and the tank is again filled with water. This process is repeated
5 times. Find out how much alcohol is left in the resulting mixture finally?

Correct Answers :

[A]

Explanation :

The amount of alcohol left = 10 x 4/5 x 4/5 x 4/5 x 4/5 x 4/5 = 10240/3125 = 2048/625

13. A vessel is full of milk 1/4 of the milk is taken out
and the vessel is filled with water. If the process is repeated 4 times and 100 liters of milk is finally left
in the vessel, what is the capacity of the vessel?

Correct Answers :

[C]

Explanation :

Let the quantity of milk initially be Q.

Then we have
Q x ¾ x ¾ x ¾ x ¾ = 100 --> Q = 25600/81 liters.

14. In what ratio should two qualities of tea having the
rates of Rs. 40 per kg and Rs. 30 per kg be mixed in order to get a mixture that would have a rate ofRs
35per kg?

Correct Answers :

[B]

Explanation :

The ratio would be 1:1 as seen from the figure:

15. Raman steals four gallons of liquid soap kept in a
train compartment’s bathroom from a container that is full of liquid soap. He then fills it with water to
avoid detection. Unable to resist the temptation he steals 4 gallons of the mixture again, and fills it with
water. When the liquid soap is checked at a station it is found that the ratio of the liquid soap now left
in the container to that of the water in it is 36: 13.

What was the initial amount of the liquid soap in the container if it is known that the liquid soap is neither used nor augmented by anybody else during the entire period?

What was the initial amount of the liquid soap in the container if it is known that the liquid soap is neither used nor augmented by anybody else during the entire period?

Correct Answers :

[D]

Explanation :

It can be seen from the ratio 36:13 that the proportion of liquid soap to water is 36/49 after two mixings. This means that 6/7th of the liquid soap must have been allowed to remain in the container and hence 1/7th of the container’s original liquid soap, would have been drawn out by the thief. Since he takes out 4 gallons every time, there must have been 28 gallons in the container. (as 4 is 1/7th of 28).

16. In what ratio should water be mixed with soda costing
Rs.12 per litre so as to make a profit of 50% by selling the diluted liquid at Rs.15 per litre?

Correct Answers :

[C]

Explanation :

In order to sell at a 50% profit by selling at `15 the
cost price should be 10. Also since water is freely available, we can say that the ratio of water and
soda must be 1:5 as can be seen from the alligation figure.

Hence, option (c) is correct.

17. A sum of Rs. 4 is made up of 20 coins that are either
10 paise coins or 60 paise coins. Find out how many 20 paise coins are there in the total amount.

Correct Answers :

[C]

Explanation :

The average value of a coin is 20 paise and there are
only 10 paise and 60 paise coins in the sum. Hence, the ratio of the number of 10 paise coins to 60 paise
coins would be 4: 1.

Since there are a total of 20 coins, the number of 10 paise coins would be 4 x 20/5 = 16 coins.

18. Pinku a dishonest grocer professes to sell pure butter
at cost price, but he mixes it with adulterated fat and thereby gains 25%. Find the percentage of adulterated
fat in the mixture assuming that adulterated fat is freely available.

Correct Answers :

[A]

Explanation :

The ratio of mixing would be 1:4 which means that the percentage of adulterated fat would be 20%.

19. A mixture of 75 liters of alcohol and water contains
20% of water. How much water must be added to the above mixture to make the water 25% of the
resulting mixture?

Correct Answers :

[A]

Explanation :

In the 15:1 ratio since, 15 corresponds to 75 liters, 1
would correspond to 5 liters. We should mix 5 liters of water.

20. A mixture of 40 liters of milk and water contains
10% water. How much water should be added to it to increase the percentage of water to 25%?

Correct Answers :

[D]

Explanation :

Average speed = In 40 liters there is 4 liters water and 36 liters milk. If we mix 8 liters of water to this (from option d); we would get a mixture containing 36 liters milk and 12 liters water – giving us the required 75% milk in the mixture. Hence, option (d) is correct.

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