**Q1. Two numbers are respectively 19% and 70% more than a third number. What percentage is the first number out of the second?**

**(a) 70**

(b) 50

(c) 90

(d) 80

**Sol.**

**Let the third number be 100.**

**Then, the first number is 100 + 19 = 119 and the second number is 170.**

**∴ The first is 119/170×100=70% of the second.**

**Q2. 20% of the populations in a town are females. If there are 72,000 males, how many females are there? If there are no eunuchs in the town.**

(a) 14400

(b) 27000

(c) 36000

**(d) 18000**

**Sol.**

**Let the total population in town = 100x**

**Male population = 80x**

**Female population = 20x**

**So, total female population =72000/4=18000**

**Q3. Mr Moron calculates his profit percentage as a percentage on selling price. He sells an item for Rs. 150 and calculates his profit percentage to be 20%. What is the true profit percentage?**

(a) 15%

(b) 20%

**(c) 25%**

(d) 35%

**Sol.**

**Sell price = 150**

**Profit =20/100×150 (According to question)**

**= 30 rupees**

**So cost profit = 150 – 30 = 120 rupees**

**True profit % =(Profit )/(Cost price )×100**

**=30/120×100=25%**

**Q4. When the selling price of a watch is Rs. 130, the loss percentage is 25%. What is the loss or gain percentage if selling price is increased to Rs. 182?**

(a) 10%

**(b) 5%**

(c) 20%

(d) 16.6%

**Sol.**

**Selling price = 130 rupees**

**Cost price =130/.75=520/3 rupees**

**When selling price Rs. 182**

**Profit % will be =((182 – 520/3 )/(520/3) ) × 100**

**=(26/520)×100 = 5%**

**Q5. Profit earned by selling an article for Rs. 1060 is 20% more than the loss incurred by selling the article for Rs. 950. At what price should the article be sold to earn 20% profit?**

(a) Rs. 10000

**(b) Rs. 12000**

(c) Rs. 13000

(d) Rs. 11000

**Sol.**

**Let the C.P of the article is x**

**According to question,**

**(1060 – x) = 1.2 × (x – 950)**

**1060 – x = 1.2x – 1140**

**1.2x = 1200**

**x = 1000 ⇒ Cost price = 1000**

**Required answer, selling price = 1000 × 1.2 = Rs. 12000**

**Q6. A class has girls and boys in the ratio 4 : 5. Among the girls, the ratio of mathematics to Physics students is 3 : 1. What percentage of the class comprises girls studying Mathematics?**

**(a) 33.3%**

(b) 25%

(c) 20%

(d) 16.6%

**Sol.**

**Let the number of boys and girls in 5x and 4x respectively.**

**Girls who studying mathematic = 3x**

**So, required percentage =3x/9x = 33.3%**

**Q7. Aditya purchases toffees at Rs. 10 per dozen and sells them at Rs. 12 for every 10 toffees. Find the gain or loss percentage.**

(a) 20%

(b) 40%

(c) 24%

**(d) 44%**

**Sol.**

**Cost price = Rs. 10/12**

**Selling price = Rs. 12/10**

**SP/CP=144/100=1.44**

**Therefore, gain percentage = 44%**

**Q8. A shopkeeper sells notebooks at the rate of Rs. 45 each and terms a commission of 4%. He also sells pencil box at the rate of Rs. 80 each and earns a commission of 20%. How much amount of commission will he earn in two weeks, if he sells 10 notebooks and 6 pencil boxes a day?**

(a) Rs. 1956

(b) Rs. 1586

(c) Rs. 1496

**(d) Rs. 1596**

**Sol.**

**Notebooks in a day, then in two weeks (i.e. 14 days) = 14 × 10 = 140 notebooks**

**Commission earned =45×4/100×140 = Rs. 252**

**6 pencil boxes in a day, then in two weeks (i.e. 14 days) = 14 × 6 = 84 pencil boxes**

**Commission earned =80×20/100×84 = Rs. 1344**

**Total commission earned = 252 + 1344 = Rs. 1596**

**Q9. The cost price of 20 articles is equal to the mark price of 15 articles. If he allowed a 10% discount on a mark price then what is the profit percentage?**

**(a) 20%**

(b) 83%

(c) 23.33%

(d) 25%

**Sol.**

**( mark price)/(cost price )=20/30=4/3**

**Mark price over the cast price is 33.3%**

**Profit factor = [(mark price factor) × (Discount factor)] – 1**

**=4/3×9/10**

**= 1.2 – 1 = .2**

**So profit percentage = 20%**

**Q10. If the difference between the CI and SI earned at the end of second year on a sum of money at the rate of 10% pa is Rs. 20, what was the sum?**

(a) Rs 3000

**(b) Rs. 2000**

(c) Rs. 2500

(d) Rs. 3500

**Sol.**

**Difference between the C.I & S.I for the two year**

**=P×r/100×r/100**

**Where r = rate of interest**

**P = total sum of money**

**20 × 100 × 100 = P × 10 × 10**

**P = 2,000**