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%
