**Q1. Lucknow bound Shatabdi Express has a capacity of 500 seats of which 10% are in the Executive class and the rest chair cars. During one journey, the train was booked to 85% of its capacity. If Executive class was booked to 96% of its capacity, then how many chair car seats were empty during that journey?**

78

Solution:

Seats for chair car = 450

Booked seats in total = 425

Booked in executive class = 48

Therefore, seats booked in chair class

= (425 – 48) = 377

Empty seats for chair class = 450 – 377 = 73

**Q2. Shobha’s Mathematics test had 75 problem i.e., 10 Arithmetic, 30 Algebra and 35 geometry problems. Although she answered 70% of the Arithmetic, 40% of the Algebra and 60% of the geometry problems correctly. She did not pass the test because she got less than 60% of the problems right. How many more questions she would have needed to answer correctly to earn a 60% passing grade?**

Solution:

= (70% of 10 + 40% of 30 + 60% of 35)

= (7 + 12 + 21) = 40

Questions to be answered correctly for 60% grade

= 60% of 75 = 45

∴ Required number of questions (45 – 40) = 5.

**Q3. 18% of A plus 15% of B plus 19% of C is equal to 17% of the sum of A, B and C. If A – B = 500 and A – C = 3400, what is the value of A + B + C?**

**Q4. In the Chidambaram’s family the ratio of expenses to the savings is 5 : 3. But his expenses is increased by 60% and income increases by only 25% thus there is a deficit of Rs. 3500 in the savings. The increased income of Mr. Chidambaram’s family is:**

**Q5. At IIM Bangalore, 60% of the students are boys and the rest are girls. Further 15% of the boys and 7.5% of the girls are getting a fee waiver. If the number of those getting a fee waiver is 90, find the total number of students getting 50% concession if it is given that 50% of those not getting a fee waiver are eligible to get half fee concession?**

Solution:

If we assume 100 students

Total: 60 boys and 40 girls.

Free waiver: 9 boys and 3 girls.

This means that a total of 12 people are getting a fee waiver. (But this figure is given as 90.)

Hence, 1 corresponds to 7.5.

Now, number of students not getting a fee waiver

= 51 boys and 37 girls

50% concession → 25.5 boys and 18.5 girls (i.e. a total of 44.)

Hence, the required answer = 44 × 7.5 = 330

**Q6. A and B have some guavas divided among themselves. A says to B “If I give you 25% of the guavas I have, I will still have 2 more guavas than you have.” To this, B says “If you give me guavas equal to 70% of what I have now, I will have 4 more guavas than you have.” What is the total number of guavas that they have?**

**Q7. The annual earning of Mr. Sikkawala is Rs. 4 lakhs per annum for the first year of his job and his expenditure was 50%. Later on for the next 3 years his average income increases by Rs. 40,000 per annum and the saving was 40%, 30% and 20% of the income. What is the percentage of his total savings over the total expenditure if there is no interest is applied on the savings for these four years:**

**Q8. A, B, C and D purchased a cine-multiplex for Rs. 56 lakhs. The contribution of B, C and D together is 460% that of A, alone. The contribution of A, C and D together is 366.66% that of B’s contribution and the contribution of C is 40% that of A, B and D together. The amount contributed by D is:**

**Q9. Ram prepares solutions of alcohol in water according to customers’ needs. This morning Ram has prepared 27 litres of a 12% alcohol solution and kept it ready in a 27 litre delivery container to be shipped to the customer. Just before delivery, he finds out that the customer had asked for 27 litres of 21% alcohol solution. To prepare what the customer wants. Ram replaces a portion of 12% solution by 39% solution. How many litres of 12% solution are replaced?**

**Q10. My friend Siddhartha Ghosh is working in the Life Insurance Corporation of India (LIC). He was hired on the basis of commission and he got the bonus only on the first years commission. He got the policies of Rs. 2 lakh having maturity period of 10 year. His commission in the first, second, third, fourth and for the rest of the years is 20%, 16%, 12%, 10% and 4% respectively. The bonus is 25% of the commission. If the annual premium is Rs. 20,000 then what is his total commission if the completion of the maturity of all the policies is mandatory:**

**Q11. Mr. Amar spends 50% of his monthly income on household items and out of the remaining he spends 25% on travelling, 30% on entertainment, 15% on shopping and remaining amount of Rs. 900 is saved. What is Mr. Amar’s monthly income?**

Solution:

Remaining = 50%

On Remaining amount he spends:-

Travelling = 25%

Entertainment = 30%

Shopping = 15%

Total = 70% ⇒ Remaining = (100 – 70) % of 50%

Rest amount ⇒ 900 = 30% of 50%

⇒ 15% = 900

100% = 6,000

**Q12. In a test consisting of 80 questions carrying one mark each, Ankita answers 65% of the first 40 questions correctly. What percent of the other 40 questions does she need to answer correctly to score 80% on the entire test?**

Solution:

Ankita scored = 65% of 40 Question (1 mark)

= 26

But she needs to score = 80% of entire ‘test’

= 80% of 80

= 64 marks

So, she needs = (64 – 26) marks

= 38

Percentage ⇒ x% of 40 = 38

⇒ x = 95

**Q13. In a class of 60 students and 5 teachers, each student got sweets that are 20% of the total number of students and each teacher got sweets that are 30% of the total number of students. How many sweets were there?**

Solution:

No. of teachers = 5

No. of sweets each students got = 20% of (60)

= 12

Total sweets distributed among students

= 12 × 60 =720

No. of sweets each teacher got = 30% of (60)

= 18

Total sweets

= 18 × 5 = 90

distributed among teachers

Total sweets = (720 + 90)

= 810

**Q14. In a college election fought between two candidates, one candidate got 55% of the total valid votes. 15% of the votes were invalid. If the total votes were 15,200, what is the number of valid votes the other candidate got?**

Solution:

Invalid = 15%

Valid votes = 85%

1st candidate = 55% of 85%

So, 2nd candidate = 45% of 85%

According to the question,

100% → 15200

85% → 12920

Other candidate got

= 45% of 12920

= 5814 vote

**Q15. On a test consisting of 250 questions, John answered 40% of the first 125 questions correctly. What percent of the other 125 questions does she need to answer correctly for her grade on the entire exam to be 60%?**