**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%