**Q1. A dishonest shopkeeper pretends to sell his goods at cost price but uses false weights and gains 11 1/9%. For a weight of 1kg he uses:**

(a) a weight of 875 gm

(b) a weight of 800 gm

(c) a weight of 950 gm

**(d) None of these**

**Sol.**

**Let the error be x gms.**

**Then, x/((100 – x) )×100=100/9**

**⇒ x/(1000 – x)=1/9**

**⇒ 9x = 1000 – x**

**⇒ 10x = 1000**

**⇒ x = 100**

**Weight used = (1000 – 100) gm = 900 gm.**

**Q2. In an examination, 65% of the total examinees passed. If the number of failures is 420, the total number of examinees is:**

(a) 500

**(b) 1200**

(c) 1000

(d) 1625

**Sol.**

**Percentage of failures = (100 – 65)% = 35%**

**Let the total number of examinees be x**

**Then, 35% of x = 420**

**⇒ 35/100×x=420**

**⇒ x=(420×100/35)=1200**

**Q3. 5% of income of A is equal to 15% of income of B and 10% of income of B is equal to 20% of income of C. If the income of C is Rs. 2000, what is the total income of A, B and C?**

(a) Rs. 14000

(b) Rs. 16000

**(c) Rs. 18000**

(d) Rs. 12400

**Sol.**

**10/100×B=20/100×C=B=2C**

**⇒ B = (2 × 2000) = 4000**

**5/100×A=15/100×B**

**⇒ A = 3B = (3 × 4000) = 12000**

**∴ (A + B + C) = Rs. (12000 + 4000 + 2000)**

**= Rs. 18000**

**Q4. A shopkeeper sold an air-conditioner for Rs. 25935 with a discount of 9% and earned a profit of 3.74%. What should have been the percentage of profit earned if no discount were offered?**

(a) 12.3%

(b) 15.6%

(c) 16%

**(d) None of these**

**Sol.**

**(91/100) × (x)=25935**

**⇒ x=(25935×100/91)=28500**

**⇒ M.P. = Rs. 28500**

**S.P. = Rs. 25935, Gain = 3.74%**

**∴ C.P. = Rs. (100/(103.74)×25935) = Rs. 25000**

**New S.P. = Rs. 28500, C.P. = Rs. 25000**

**∴ New Gain% =(3500/25000×100)%=14%**

**Q5. A typist uses a paper 30 cm by 15 cm. He leaves a margin of 2.5 cm at the top of as well as at the bottom and 1.25 cm on either side. What percentage of paper area is approximately available for typing?**

(a) 65%

**(b) 70%**

(c) 80%

(d) 60%

**Sol.**

**Total area of the paper = (30×15)cm^2**

**=450 cm^2**

**Area used =[(30-5)×(15-2.5)] cm^2**

**=(25×12.5) cm^2**

**=(25×25/2) cm^2=625/2 cm^2**

**Percentage of area used**

**=(625/2×1/450×100)%=69.5%**

**= 70% nearly**

**Q6. The ratio of the number of boys and girls is 3 : 2. If 20% of the boys and 30% of the girls are scholarship holders, then the percentage of students who do not get scholarship is:**

(a) 50

(b) 72

(c) 75

**(d) 76**

**Sol.**

**Let the number of boys 3x and number of girls be 2x**

**Number of scholarship holders**

**=(20/100×3x+30/100×2x)=6x/5**

**Number of those who do not hold scholarship**

**=(5x-6x/5)=19x/5**

**∴ Required percentage =(19x/5×1/5x×100)%=76%**

**Q7. When a number is first increased by 10% and then reduced by 10% the number:**

(a) Does not change

**(b) Decrease by 1%**

(c) Increase by 1%

(d) None of these

**Sol.**

**Let the given number be x**

**Increased number = (110% of x)**

**=(110/100×x)=11x/10**

**Finally 11x/10, reduced number**

**=(90% of 11x/10)=(90/100×11x/10)=99x/100**

**Decrease =(x-99x/100)=x/100**

**Decrease % =(x/100×1/x×100 )%=1%**

**Q8. Because of scarcity of rainfall, the price of a land decreases by 12% and its production also decreases by 4%. What is the total effect on revenue?**

(a) Loss of 16%

(b) Gain of 15%

**(c) Loss of 15.52%**

(d) Gain of 15.48%

**Sol.**

**Net effect =[-12-4+(-12)(-4)/100]% = (–16 + 0.48)% = –15.25%**

**Q9. From 1980-1990, the population of a country was increased by 20%.**

**From 1990 – 2000, the population of the country was increased by 20%**

**From 2000-2010, the population of the country was increased by 20%**

**Then the overall increased population (in percentage) of the country from 1980-2010 was**

(a) 60%

(b) 62.8%

(c) 72.2%

**(d) 72.8%**

**Sol.**

**Let the population in the year 1980 = x**

**Then, the population in the year 1990 = 120% of x**

**Then, the population in the year 2000**

**= 120% of 120% of x**

**And the population in year 2010**

**= 120% of 120% of 120% of x**

**=6/5×6/5×6/5×x=216/125 x**

**Hence, required percentage**

**=(216/125 – x)/x×100%**

**=91/125×100%=72.8%**

**Q10. An article passing through two hands is sold at a profit of 38% at the original cost price. If the first dealer makes a profit of 20%, then the profit percent made by the second is:**

(a) 5%

(b) 10%

(c) 12%

**(d) 15%**

**Sol.**

**Let the C.P. be Rs. 100**

**Then, S.P = Rs. 138**

**Let the profit made by 2nd dealer be x%**

**Then, (100 + x)% of 120% of Rs. 100 = Rs. 138**

**⇒ ((100 + x))/100×120/100×100=138**

**⇒ 6(100 + x) = 690**

**⇒ 6x = 90 ⇒ x = 15**

**∴ Required% = 15%**