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.
