Averages, ratio and proportions is an important arithmetic topic in CAT. The number of questions from this topic has increased by a great margin in the recent years. The subtopics that fall under this topic are averages, percentages, ratios and proportion, mixtures and alligations. Go through the questions with solutions given below to enhance your understanding of the topic.

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Instructions

For the following questions answer them individually

Question 1

There are 25 students in a class and the number of students who scored 5, 7 and 3 marks in a test are 8, 10 and 7 respectively.

The teacher can decide how many students should go to the remedial class, but can't pick the students for it. Once the number is decided, the students are selected at random. The teacher wants every student in the class to have atleast three others who scored the same marks in the examination. What is the minimum number of students who should be sent to the remedial class for this to happen?

Question 2

There are 11 participants in an under-19 competition ( Participants can be up to 19 years old ) . The average age of the group is 13 years. Leaving out the youngest and the oldest, the others are divided into 3 groups of 3 each, such that the average ages of the 3 groups are 11, 13 and 14 years respectively. What is the maximum difference between the ages of the youngest and oldest participants? (All the ages are integers)

Question 3

A, B and C are 3 varieties of beer which contains starch, hops and water in varying proportions. A contains x% starch and y% hops. B contains y% starch and y% water. C contains x% hops and y% water. When A, B and C are mixed in the ratio 2:3:5, then the final mixture has 38% starch and 28% hops. Find the sum of x and y?

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Question 4

A rice trader selling basmati rice makes a profit on the trade by adulterating the rice with an inferior substitute surti kolam. When he mixes the basmati and kolam in the ratio 3:2 he makes a profit of 33.33%. When he mixes them in the ratio 4:1 he makes a profit of Rs 25 per kg. In what ratio must he mix the two rices to make a profit of 100%? (Assume he sells at the stated price of basmati per kg)

Question 5

The ratio of incomes of Anil and Ajit is 5:7. The ratio of their expenditures is 3:4, then which of the following is a possible ratio of the savings? (Savings = Income - Expenditure)

Question 6

A shopkeeper buys 3 varieties of rice for Rs 20, Rs 30 and Rs 40 per kg respectively. He now mixes the 3 varieties in the ratio 5:6:7 by weight and sells the mixture at a profit of 10%. What price does he sell it for?

Question 7

The price of a watch is marked up by 40% on its previous selling price and a discount of 50% is offered on the marked up price. If the profit made after the discount is 20%, find the profit made on the watch (in percentage) if the discount offered was 25%.

(If the answer is a%, enter a as your answer).

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Question 8

Two alloys are such that the ratio of iron to copper in the first alloy is 7:13 and that in the second alloy is 5:12. In what ratio should the two alloys be mixed such that resulting alloy has copper and iron in the ratio 7:3.

Question 9

The average weight of a class of students is 24 kgs. 5 students who together weigh 140 kgs leave the class and 2 students who together weigh 68 kgs join the class. What is the new average of the class?

Question 10

In a class consisting of 150 students, one more student is added and as a result the average weight of class increases by 0.05. From this class one student is taken out and the average weight of the class is reduced by 0.02. If the sum of the weights of the two students mentioned is 2x+b, where x is the original average weight of the class of 150 students, then find the value of b.

Question 11

A, B, C, D, E and F are six different natural numbers in ascending order. There were 15 numbers - 10, 15, 17, 13, 19, 18, 16, 20, 15, 13, 17, 11, 24, 22, and 20 - on a paper. Each of those 15 numbers were sum of 2 numbers taken at a time among A, B, C, D, E and F. Which of the following could be the value of C?

Question 12

Ram added some water to the solution of juice and water such that the initial ratio a/b of juice to water gets inverted. Shyam sees Ram adding the water and he adds the juice to the solution such that the ratio of juice to water is back to its initial value. What is the possible value of ratio of amount of juice in the original solution to the final solution if both a and b are natural numbers?

Question 13

There are three taps A, B, C in a tank. Initially A and B are opened. A fills milk at the rate of 4 L/min and B fills water at the rate of 2 L/min. When the tank is 50% full, tap C is opened. Tap C fills milk at the rate of x L/min. If the concentration of milk is 80% when the tank is full, find the value of x (in L/min)?

Question 14

Ironite, a form of iron is extracted from an iron ore that contains iron and zinc in the ratio 3:2 by weight. In the process of extraction, some amount of zinc is lost. If ironite contains 10% zinc by weight, find the amount of ore needed to produce 5 tonnes of Ironite.

Question 15

Three students A, B, C stole some candies. As it was late in the evening, they decided to divide the candies equally among themselves in the morning and went to sleep. During the night, A woke up, ate one candy, then took one third of the remaining candies and went back to sleep. After some time B woke up, ate one candy, then took one third of the remaining candies and went back to sleep. Lastly, C woke up and did the same as other two, that is, ate one candy and then took one third of the remaining candies. When all three woke up in the morning, they found that the total number of candies were in the form 3k+1. Find the minimum number of candies that were present initially.

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Question 16

Three friends Lohit, Mohit and Nohit have Rs. 120 together. Lohit gives Mohit an amount which Mohit already has; Mohit then gives Nohit an amount which Nohit already has; Nohit then gives Lohit an amount which Lohit already has. In the end all of them have equal amounts with them. What is the amount which Lohit originally had?

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Question 17

‘n’ years later the sum of ages of Messi and Maradona will be 80. ‘n’ years ago the age of Maradona was 3 times that of Messi. ‘2n’ years ago the age of Maradona was 4 times that of Messi. What will be the difference in their ages after ‘2n’ years from the present?

Question 18

In what ratio should three salt solutions of concentrations 15%, 20% and 30% be mixed, so that the resultant solution is of concentration 25% ?

Question 19

Lokesh bought Grapes, Milk and Sugar in the ratio of 8:5:3. Further, he knows that grapes are 60% water and milk is 80% water. He put everything together and cooked the mixture for 2 hours during which 25% of the water in the dish got evaporated. What is the ratio of dry grapes to water in the cooked dish? (All ratios and percentages are to be taken by weight)

Question 20

The price of a iPhone is increased by 15% and then decreased by 10%. The price of an iPod is increased by 10% and then decreased by 15%. If the final prices of both the items are the same, find the ratio of the initial price of iPhone to the initial price of iPod.

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