Mostly 2 to 3 questions will appear in CAT exam every year on Averages, Ratio and proportion. The concepts to learn are very basic and most students who learnt this concepts well will find this topic easy. Learn Ratio and proportion concepts and formulas for CAT. We are providing one set of solved questions on this topic and this questions are very important to learn and apply the concepts of Ratios.

**Ratio and Proportion Questions For CAT:**

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**Question 1:**

The average marks of a student in 10 papers are 80. If the highest and the lowest scores are not considered, the average is 81. If his highest score is 92, find the lowest.

**a)** 55

**b)** 60

**c)** 62

**d)** Cannot be determined

Question 2:

The last time Rahul bought Diwali cards, he found that the four types of cards that he liked were priced Rs.2.00, Rs.3.50, Rs.4.50 and Rs.5.00 each. As Rahul wanted 30 cards, he took five each of two kinds and ten each of the other two, putting down the exact number of 10 rupees notes on the counter payment. How many notes did Rahul give?

**a)** 8

**b)** 9

**c)** 10

**d)** 11

Question 3:

One bacterium splits into eight bacteria of the next generation. But due to environmental condition only 50% survives and remaining 50% dies after producing next generation. If the seventh generation number is 4,096 million, what is the number in first generation?

**a)** 1 million

**b)** 2 million

**c)** 4 million

**d)** 8 million

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**Question 4:
**

You can collect as many rubies and emeralds as you can. Each ruby is worth Rs. 4 crore and each emerald is worth Rs. 5 crore. Each ruby weighs 0.3 kg. And each emerald weighs 0.4 kg. Your bag can carry at the most 12 kg. What should you collect to get the maximum wealth?

**a)** 20 rubies and 15 emeralds

**b)** 40 rubies

**c)** 28 rubies and 9 emeralds

**d)** None of these

**QuestionÂ 5:**

My son adores chocolates. He likes biscuits. But he hates apples. I told him that he can buy as many chocolates he wishes. But then he must have biscuits twice the number of chocolates and should have apples more than biscuits and chocolates together. Each chocolate cost Re 1. The cost of apple is twice the chocolate and four biscuits are worth one apple. Then which of the following can be the amount that I spent on that evening on my son if number of chocolates, biscuits and apples brought were all integers?

**a)** Rs. 34

**b)** Rs. 33

**c)** Rs. 8

**d)** None of these

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**Solutions for Ratio and proportionÂ questions : 1 to 5**

**1)**Â Answer (b)

Total marks = 80Ã—10=800

Total marks except highest and lowest marks = 81Ã—8 = 648

So Summation of highest marks and lowest marks will be = 800 – 648 = 152

When highest marks is 92, lowest marks will be = 152-92 = 60

**2)**Â Answer (d)

According to question Rahul put exact number of 10 rs. notes, hence total price will be a multiple of 10.

And Rahul wants 30 cards, where he took 5 each of two kind and 10 each of other two kind.

So summation of (price of one type card multiplied by number of that type of card) should be a multiple of 10.

By looking at the prices of cards and to make the sum a multiple of 10, we can say that two 5 cards were of rs. 3.5 and 4.5 and two 10 cards were of prices 2 rs.and 5 rs each respectively.

Hence total sum will be 5 Ã— (3.5+4.5) + 10 Ã— (2+5) = 110

So rahul gave 11 notes of 10 rs.

**
3)Â **Answer (a)

let’s say x is the initial number of bacterias :

So in 2nd generation no. of bacterias = 8x/2 = 4x

In 3rd generation, it will be = 16x

4th gen. = 64x

5th gen. = 256x

6th gen. = 1024x

7th gen. = 4096x

Hence x = 1 million

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**4)**Â Answer (b)

Let’s say number of rubbies are x and emeralds are y.

So 0.3x + 0.4y = 12

And total wealth = 4x+5y

Now putting value of x from eq.1 to eq.2

i.e. total wealth = 4(12-0.4y)/0.3 + 5y

Now for maximizing total wealth y should be equal to zero.

Hence x = 40

**5)Â **Answer (a)

When numbers of chocolates, biscuits and apples are integers.

Now let’s say number of chocolates taken 1 , then biscuits will be 2 and apples can be 4,5,6,7

Hence minimum money that should be spent = 1+1+8 = 10 (Hence option C is cancelled)

Now when number of chocolates are 4

Biscuits will be 8

And apples can be 13,14,15….

Now total money spent can be 4+4+26 = 34 and more of it.

Hence answer will be A

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