MAT PO CAT

# Quantitative Aptitude

## SOLVING FROM OPTION

Questions which are asked in competitive examinations are generally simple questions. Any student with normal aptitude in mathematics and logics can easily solve these questions if the student has the luxury of time. But more often than not, time comes at a premium in competitive examinations. You generally need to solve 50 questions in 30 minutes. For majority of the students, it is a daunting task.

But, is there a way out? Yes, if you think innovatively; you can solve most of the questions within no time. One way of doing this is solving by using options as tools. Some other questions may require you to follow an unconventional approach. A very few questions would need to be solved by conventional methods.

In this section, we have tried to combine all these approaches to solve questions. Hope, these methods would prove to be highly helpful for you.

Question 1. A trader calculates his profit on the selling price and says it to be 20%. Find the actual profit.

- 18%
- 20%
- 25%
- 30%

**Answer:** Since profit has been calculated on selling price instead of on cost price, so correct percentage profit will be more than the calculated profit. This means that options ‘a’ and ‘b can be easily ruled out. This leaves us with options ‘c’ and ‘d’.

Let us, proceed by using the option ‘c’, i.e. 25%.

If Cost Price = Rs. 100

Then profit = Rs. 25

Then, Selling Price = Rs. 125

Now, 25 is 20% of Rs. 125; which is matching with the figure in question.

Hence, option ‘c’ is the right answer.

Question 2. A trader sold a television set for Rs. 27,500 and gained 10%. Find the cost price of the television.

- 25000
- 22500
- 24750
- 22750

**Answer:** Let us start with solving through option ‘a’, i.e. 25000

10% of 25000 = 2500

And, 25000 + 2500 = 27500 which is matching with the figure in question. Hence, option ‘a’ is the right answer.

Question 3. A shopkeeper claims to sell rice at the cost price but he weighs only 1200 grams for every 1350 grams. What is the profit percentage of the trader?

- 12.5%
- 15%
- 17.5%
- 20%

**Answer:** Let us assume cost price to be Re. 1 per gram. This means;

CP of 1200 g = Rs. 1200

Since he weighs only 1200 g for every 1350 g, so he is selling 1200 g at CP of 1350 g

This means that he is earning a profit of Rs. (1350 – 1200) = Rs. 150 on this quantity.

Now, 10% of 1200 = 120

This leaves (150 – 120) = 30

30 is 2.5% of 1200

Hence, profit = 10 + 2.5 = 12.5%

Question 4. The selling price of 40 articles is equal to the cost price of 45 articles. What is the profit or loss percentage?

**Answer:** An easy way to solve this question is by taking LCM of 40 and 45

LCM of 40 and 45 = 360

Let us assume; CP of 45 articles = Rs. 360

As per question; SP of 40 articles = Rs. 360

So, SP of 45 articles = Rs. 405

So, profit = 405 – 360 = Rs. 45

Hence, percent profit `= (45)/(360)xx100 = 12.5%`

Question 5. The ratio of two numbers is 3:4. If 12 is added to each of the two numbers, the ratio becomes 5:6. What is the sum of the two numbers?

- 32
- 42
- 52
- 66

**Answer:** The ratio says that numbers are respectively divisible by 3 and 4. It also says that their sum is divisible by (3 + 4) = 7. Only one option, i.e. option ‘b’ is divisible by 7. So, ‘b’ is the right answer.

You can cross check your answer as follows:

`3x + 4x = 42`

Or, `7x = 42`

Or, `x = (42)/7 = 6`

So, numbers are; `3x = 18` and `4x = 24`

Add 12 to each number and you will get 30 and 36

Now,`(30)/(36) = 5/6` which is matching with the figure in question.

Question 6. If a:b = 1:2, b:c = 6:5 and c:d = 2:3, find a:d.

- 2:5
- 5:2
- 3:5
- 1:3

**Answer:** `a/b = 1/2` and `b/c = 6/5`

So, `b = 2a` and `b = (6c)/5`

Or, `2a = (6c)/5`

Or, `a = (3c)/5`

Or, `c = (5a)/3`

Now, we have `c/d = 2/3`

Or, `c = (2d)/3`

From this and previous equation; `(5a)/3 = (2d)/3`

Or, `5a = 2d`

Or, `a/d = 2/5`

So, option ‘a’ is the right answer.

Question 7. The ratio of two positive integers is 7:5. Their difference is 12. What is the sum of the numbers?

- 24
- 72
- 36
- 48

**Answer:** Difference in ratio = 7 – 5 = 3

Actual difference = 12 which is 4 times the difference in ratio

Hence, sum of the numbers can be calculated as follows: `4(7 + 5) = 4 xx 12 = 48`

So, option ‘d’ is the right answer.

Question 8. If Arun’s monthly salary is 25% more than the monthly salary of Bhupathi, then by what percentage is the monthly salary of Bhupati less than that of Arun?

- 10% .
- 12%
- 15%
- 20%

**Answer:** If Bhupati’s salary is 100 then Arun’s salary is 125

Now, 100 is 20% less than 125

So, option ‘d’ is the right answer.

Question 9. 20 kg rice of price Rs. 15 per kg is mixed with 30 kg rice of prices Rs. 12 per kg. What is the average price of the mixture?

- 13
- 13.50
- 13.20
- 13.60

**Answer:** In this case, you need to calculate by conventional method;

`20 xx 15 + 30 xx 12 = 300 + 360 = 660` is the price of 50 kg rice

So, price of 1 kg rice `= (660)/(50) = 13.20`

Question 10. The average amount with a group of nine members is Rs. 45. Another six members joined the group with each having Rs. 40. What is the average amount with the members in the group now?

- 39
- 41
- 43
- 45

**Answer:** In this case, you need to calculate by conventional method;

`9 xx 45 + 6 xx 40 = 405 + 240 = 645` is the amount with 15 people

So, average amount per people `= (645)/(15) = Rs. 43`

So, option ‘c’ is the right answer.