**Q1. A dishonest dealer professes to sell at cost price but uses a 900 gram weight instead of 1-kilogram weight. Find the percent profit to the dealer.**

**(a) 11.11%**

(b) 14%

(c) 12.13%

(d) 15%

Sol.

Let the cost price be x Rs. per kg.

Then cost price of 900 gn =9/10 x

Hence % profit

=(x – 9/10 x)/(9/10 x)×100=100/9%=11.11%

**Q2. The Average age of a class of 22 students is 21 years. The average increased by 1 when the teacher’s age also included. What is the age of the teacher?**

(a) 48

(b) 45

(c) 43

**(d) 44**

Sol.

Total age of all students = 22×21

Total age of all students + age of the teacher = 23 × 22

Age of the teacher = 23×22 – 22×21 = 22(23-21) = 22×2 = 44

**Q3.My brother is 3 years elder to me. My father was 28 years of age when my sister was born while my mother was 26 years of age when I was born. If my sister was 4 years of age when my brother was born, then what was the age my father when my brother was born?**

(a) 35 years

(b) 34 years

(c) 33 years

**(d) 32 years**

Sol.

Let my age = x

My mother’s age = x + 26

My sister’s age = (x + 3) + 4 = x + 7

My Father’s age = (x + 7) + 28 = x + 35

=> age my father when my brother was born

= x + 35 – (x + 3) = 32

**Q4. The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).**

(a) 8, 20, 28

**(b) 16, 28, 36**

(c) 20, 35, 45

(d) None of these

Sol.

Let their present ages be 4x, 7x and 9x years respectively.

Then, (4x – 8) + (7x – 8) + (9x – 8) = 56

=> 20x = 80

=> x = 4.

So Their present ages are 4x = 16 years,

7x = 28 years and 9x = 36 years respectively.

**Q5.The ages of two persons differ by 16 years. 6 years ago, the elder one was 3 times as old as the younger one. What are their present ages of the elder person?**

(a) 10

(b) 20

**(c) 30**

(d) 40

Sol.

Let’s take the present age of the elder person = x and the present age of the younger person

= x – 16

(x – 6) = 3 (x-16-6)

=> x – 6 = 3x – 66

=> 2x = 60

=> x = 60/2 = 30

**Q6. Mr. Ravi spent 20% of his monthly income on food and 15% on children’s education, 40% of the remaining he spent on entertainment and transport together and 30% on medical. He is left with an amount Rs. 8775 after all these expenditures. What is Mr. Ravi’s monthly income?**

(a) Rs. 40,000

(b) Rs. 35,000

**(c) Rs. 45,000**

(d) Rs. 38,000

Sol.

let total monthly income of ravi =X

X of 30% of 65% = 8775 ⇒

=(8775 × 100 × 100)/(30 × 65)= Rs. 45,000

**Q7. In a class of 35 students and 6 teachers, each student got toffees that are 20% of the total number of students and each teacher got toffees that are 40% of the total number of students. How many toffees were there?**

(a) 245

(b) 161

(c) 406

**(d) 329**

Sol.

35 × 20% of 35 + 6 × 40% of 35

245 + 84 = 329

**Q8. If the height of a cylinder is increased by 15% and the radius of its base is decreased by 10%, then by what percent will its curved surface area change?**

(a) 3.5% decrease

**(b) 3.5% increase**

(c) 5% increase

(d) 5% decrease

Sol.

H1=100 H2=115

R1=100 R2=90

Curved surface area =πrh

π R1 H1 π R2 H2

⇒ 100 × 100 ⇒ 115 × 90

⇒ 10,000 ⇒ 10350

⇒ 200 ⇒ 207

Increase = 207 – 200 = 7

% increase =increase/original×100%

=7/200×100=3.5%

**Q9. A house and a shop were sold for Rs. 1 lakh each. In this transaction, the house sale resulted into 20% loss whereas the shop sale resulted into 20% profit.The entire transaction resulted in**

(a) No loss no gain

(b) Gain of Rs. 1/24 lakh

**(c) Loss of Rs. 1/12 lakh**

(d) Loss of Rs. 1/18 lakh

Sol.

Total S.P. = Rs. 2 lakhs

C.P. =100/(100 – L%)×S.P.

C.P of house = Rs. (100/80×1) lakh

= Rs. 5/4 lakh

C.P. =(100 )/(100-P%)×S.P.

C.P. of shop =Rs.(100/120×1) lakh =Rs.5/6

Total C.P. = Rs. (5/4+5/6) lakhs

= Rs. 25/12 lakhs

∴ Loss = Rs. (25/12-2) lakh = Rs. 1/12 lakh

**Q10. A ruby stone was bought for Rs.1600 at Jaipur. A sum of Rs.2400 was spent on making a ring with the ruby stone. It was advertised for sale of Bombay for Rs.7800. If a discount of 10% was given, then the percentage profit made was:**

(a) 55%

(b) 68.5%

**(c) 75.5%**

(d) 80%

Sol.

cost price of Rubi stone = Rs.1600

cost price of Ring = Rs.2400

Actual cost price = Rs. 4000

Selling price = (7800*90/100)= 7020

profit percent = (7020-4000)/4000 *100=75.5%