**Q1. The sum of number and its reciprocal is one-fifth of 26. What is the number?**

(a) 3

(b) 4

**(c) 5**

(d) 6

**Sol.**

**Let the number be x. Then,**

**x+1/x=26/5⇒(x^2 + 1)/x=26/5⇒5x^2-26x+5=0**

**⇒ (x-5)(5x-1)=0⇒x=5 or 1/5**

**Q2. A number divided by 899 gives a remainder of 63. If the number is divided by 29, the remainder will be**

(a) 2

**(b) 5**

(c) 13

(d) 28

**Sol.**

**If a number x is divided by 899 gives a remainder 63 and quotient y.**

**∴ x = y × 899 + 63 ⇒ x = (31y + 2) × 29 + 5**

**It is clear from above that if x is divided by 29 then the remainder is 5.**

**Q3. In a college, 200 students are there in which 36% are girls. Each boy’s monthly fees is Rs. 480 and each girl paid 25% less monthly fees in comparison to boy. What is the total monthly fees amount paid by boys and girls?**

(a) Rs. 873400

(b) Rs. 867300

(c) Rs. 876300

**(d) Rs. 873600**

**Sol.**

**Number of girls in a college =2000×36/100=720**

**Then, boys = 2000 – 720 = 1280**

**Each girl’s monthly fees =480×75/100 = Rs. 360**

**Hence, total amount of fees both boys and girls**

**= (1280 × 480 + 720 × 360) = Rs. 873600**

**Q4. Raman scored 456 marks in an exam and Seeta got 54% marks in the same exam is 24 marks less than Raman. If the minimum passing marks in the exam is 34%, then how much more marks did Raman score then the minimum passing marks?**

**(a) 184**

(b) 196

(c) 190

(d) 180

**Sol.**

**Let the total marks of the exam be x.**

**Then,**

**x×54/100=456-24**

**=x×54/100=432**

**⇒x=(432 × 100)/54=800**

**∴ Minimum passing marks =800×34/100=272**

**Hence, required more marks get by Raman = 456 – 272 = 184**

**Q5. If the cost price of 12 articles be equal to the selling price of 10 articles, then find the profit per cent in the transaction.**

(a) 15

**(b) 20**

(c) 25

(d) Data insufficient

**Sol.**

**Let the CP of 1 articles = Rs. 1**

**Then, CP of 12 articles = Rs. 12 = SP of 10 articles**

**Also, CP of 10 articles = Rs. 10**

**Profit percent =(2/10×100)%=20%**

**Q6. A grocer purchased 75 kg of sugar at Rs. 30 per kg and mixed it with 25 kg of sugar at Rs. 36 per kg. At what rate should he sell the mixture to gain 10%?**

(a) Rs. 32.20

(b) Rs. 32.45

(c) Rs. 32.60

**(d) None of these**

**Sol.**

**CP of 100 kg of mixture = (75 × 30 + 25 × 36) = Rs. 3150**

**SP = 110% of 3150 =(110/100×3150) = Rs. 3465**

**Rate of SP of the mixture =(3465/100) = Rs. 34.65**

**Q7. Rehaan purchased a bike for Rs. 54000. He sold it at a loss of 8%. With that money he again purchased another bike and sold it at a profit of 10%. What is his overall loss/profit?**

(a) Loss of Rs. 657

(b) Profit of Rs. 567

(c) Loss of Rs. 648

**(d) Profit of Rs. 648**

**Sol.**

**Cost price = Rs. 54000**

**Selling price = 54000×((100-8))/100 = Rs. 49680**

**Now, the cost price of another bike = Rs. 49680**

**Selling price of another bike = 49680×110/100 = Rs. 54648**

**Overall profit = 54648 – 54000 = Rs. 648**

**Q8. 6 bells commence tolling together and toll of intervals are 2, 4, 6, 8, 10 and 12 s, respectively. In one hour, how many times do they toll together?**

(a) 16

(b) 32

(c) 21

**(d) 31**

**Sol.**

**LCM of 2, 4, 6, 8, 10, 12 = (2 × 2 × 3 × 2 × 5) = 120**

**∴ After every 2 min they toll together**

**∴ Number of times they toll together in one hour**

**=(60/2+1) times = 31 times**

**Q9. A certain type of board is sold in lengths of multiples of 2 ft. the shortest board sold is 6 ft and the longest is 24 ft. A builder needs a large quantity of these types of board in 5 1/2 ft lengths. Find the length of be ordered for which waste is minimum.**

(a) 24 ft

(b) 26 ft

**(c) 22 ft**

(d) 52 ft

**Sol.**

**LCM of (2 and 5 1/2) = LCM of (2 and 11/2)**

**Required answer =(LCM of 2 and 11)/(HCF of 1 and 2)=22/1 = 22 ft**

**Q10. The average expenditure of a man for the first 12 days of a month was Rs. 850 per day and for the next 18 days, it was Rs. 825 per day. If he could save Rs. 700 during that month. Find his income for the month.**

(a) Rs. 22650

(b) Rs. 29450

(c) Rs. 24150

**(d) Rs. 25750**

**Sol.**

**Expenditure for the first 12 days (850 × 12) = Rs. 10200**

**Expenditure for the next 18 days = (825 × 18) = Rs. 14850**

**Savings = Rs. 700**

**∴ Income for the month = (10200 + 14850 + 700) = Rs. 25750**