Q1. Rs. 395 are divided among A, B and C in such a manner that B gets 25% more than A and 20% more than C. The share of A is:
(a) Rs. 198
(b) Rs. 120
(c) Rs. 180
(d) Rs. 195
Sol.
Suppose A get Rs. x
Then B gets 125% of
x=125/100×x=Rs.5x/4
If B gets Rs. 120
Then C gets Rs. 100
If B gets Rs. 5x/4
Then C gets
= Rs. (100/120×5x/4) = Rs. 25x/24
∴ x+5x/4+25x/24=395
⇒ (24x + 30x + 25x) = (395 × 24)
⇒ 79x = (395 × 24)
⇒ x=((395 × 24)/79)=120
Hence, A gets Rs. 120
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. 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%
Q4. 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
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. A dishonest shopkeeper pretends to sell his goods at cost price but uses false weights and gains 11 1/9%. For a weight of 1 kg 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.
Q7. 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%
Q8. The marked price of a shirt and trousers are in the ratio 1 : 2. The shopkeeper gives 40% discount on the shirt. If the total discount on both is 30%, the discount offered on the trousers is:
(a) 15%
(b) 20%
(c) 25%
(d) 30%
Sol.
Let the M.P; of shirt be Rs. x and that of trousers be Rs. 2x
Let y% be the discount on trousers.
Then, 60/100×x+(100 – y))/50×2x=70/100×(x+2x)
⇒ 3/5+((100 – y))/50=21/10
⇒ ((100 – y))/50=(21/10-3/5)=15/10=3/2
⇒ (100-y)=(3/2×50)=75
⇒ y = 25
Q9. 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%
Q10. A fan is listed at Rs. 1500 and a discount of 20% is offered on the list price. What additional discount must be offered to the customer to bring the net price to Rs. 1104?
(a) 8%
(b) 10%
(c) 12%
(d) 15%
Sol.
Let additional discount be x%
Then, 80% of (100 – x)% of Rs. 1500 = Rs. 1104
⇒ 80/100×((100-x))/100×1500
⇒ 12x = (1200 – 1104) = 96
⇒ x = 8
∴ Additional discount = 8%
