**Q1. The sum of the digits of a two- digit number is 9. If 9 is added to the number, then the digits are reversed. Find the number.**

(a) 36

(b) 50

(c) 45

(d) 54

**Q2. If a piece of rod is 3000 m and we have to supply some lampposts. One lamppost is at each end and distance between two consecutive lamp-post is 75 m. Find the number of lampposts required.**

(a) 41

(b) 39

(c) 40

(d) 43

**Q3. If x = 2 + √3, the value of (x^6+x^4+x^2+1)/x^3 is**

(a) 65

(b) 56

(c) 69

(d) 67

**Q4. If a = 25, b = 15, c = −10, then the value of (a^3+b^3+c^3-3abc)/((a-b)^2+(b-c)^2+(c-a)^2 ) is**

(a) 30

(b) −15

(c) −30

(d) 15

**Q5. A shopkeeper sells his goods at 15% discount. The marked price of an article whose selling price is Rs. 629, is**

(a) Rs. 740

(b) Rs. 704

(c) Rs. 700

(d) Rs. 614

**Q6. In a 100 m race, A beats B by 10 m and C by 13 m. In a race of 180 m, B will beat C by**

(a) 4.5 m

(b) 5.4 m

(c) 5 m

(d) 6 m

**Q7. A cistern has two pipes. One can fill it with water in 8 hours and the other can empty it in 5 hours. In how many hours will the cistern be emptied if both the pipes are opened together when (3/4) th of the cistern is already full of water?**

(a) 10/3 hours

(b) 6 hours

(c) 10 hours

(d) 40/3 hours

**Q8. Ram, Shyam and Kamal together started a business in partnership. The ratio of their capitals is 3 : 4 : 7. If their annual profit be Rs. 21000, what will be Kamal’s share in this profit?**

(a) Rs. 12500

(b) Rs. 10500

(c) Rs. 15000

(d) Rs. 10000

**Q9. If the interest is payable annually, then the principal on which the compound interest for 3 years at 10% p.a. is Rs. 331, is given by:**

(a) Rs. 900

(b) Rs. 1000

(c) Rs. 1050

(d) Rs. 1100

**Q10. Fifteen years hence, a man will be just four times as old as he was 15 years ago. His present age is**

(a) 10 years

(b) 15 years

(c) 20 years

(d) 25 years

**Solutions**

S1. Ans.(c)

Sol. Let the unit’s place digit be x and ten’s place digit by,

x + y = 9

and (10y + x) + 9 = (y + 10x)

On solving Equation (i) and (ii), we get x = 5 and y = 4.

Hence, required number is 45.

S2. Ans.(a)

Sol. Number of lampposts required = 3000/75 + 1

= 40 + 1 = 41

S5. Ans.(a)

Sol. Let marked price = x

According to the question,

x × 85/100 = 629

∴ x = (629 × 100)/85 = Rs. 740

S6. Ans. (d)

Sol. A : B : C = 100 : 90 : 87

∴B/C=90/87=(90 × 2)/(87 × 2)=180/174

Thus, while B covers 180 m, C covers 174 m.

∴ B beats C by 6 m.

S7. Ans.(c)

Sol. Net part emptied by both in 1 hr

=((1/5)-(1/8))=3/40

3/40 part is emptied in 1 hr.

3/4 part will be emptied in = (40/3)×(3/4) = 10 hours.

S8. Ans.(b)

Sol. Ram : Shyam : Kamal = 3 : 4 : 7

Kamal’s share = 21000×(7/14) = Rs. 10500

S10. Ans.(d)

Sol. Let man’s present age be x years.

His age 15 years ago = (x – 15) years;

His age 15 years hence = (x + 15) years.

(x + 15) = 4(x – 15)

⇒ 3x = 75

⇒ x = 25

His present age is 25 years.