# PAR Mathematics Paper 1 for 2013

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26. Tarun travels a distance of 24km at 6 km/hr. another distance of 24km at 8 km/hr. and a third distance of 24 km at 12 km/hr. His average speed for the whole journey (in km/hr.) is

(A) 8 2/3

(B) 8

(C) 9

(D) 7

27. Rohan lends 1000 in four parts. If he gets 8% interest on 2000, 7 1/2% on 4000 and 8 1/2% on 1400 what percent of interest must he get for the remainder if his average annual interest is 8.13%?

(A) 10%

(B) 9%

(C) 8%

(D) None of these

28. A solid piece of iron is in the form of a cuboid of dimensions (49cmx33cmx24cm) is melted and molded to form a solid sphere. The radius of the sphere is

(A) 23 cm

(B) 21 cm

(C) 19cm

(D) 25cm

29. Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16cm. The diameter of each sphere is:

(A) 4cm

(B) 3cm

(C) 2 cm

(D) 6 cm

30. Perimeter of a circle is equal to the perimeter of a square whose area is 484 cm². What is the radius of the circle?

(A) 14cm

(B) 12 cm

(C) 7 cm

(D) 16 cm

31. Puneeta borrowed from Reena certain sum for two years at simple interest. Puneeta lent this sum to Venu at the same rate for two years compound interest. At the end of two years she received 110 as compound interest but paid 100 as simple interest. Find the sum and rate of interest:

(A) 250, rate 20% per annum

(B) 250, rate 25% per annum

(C) 250, rate 10% per annum

(D) None of these

32. 13 chairs and 5 tables were brought for 8280. If the average cost of the table will be 1227, what is the average cost of a chair?

(A) 2145

(B) 165

(C) 175

(D) None of these

33. A man goes uphill with an average speed of 24 kmph and comes down with an average speed of 36 kmph. The distance travelled in both the cases being the same, The average speed (in km/hr) for the entire journey is:

(A) 30.8

(B) 32.8

(C) 28.8

(D) None of these

34. 40% of the employees of a certain company are men, and 75% of the men earn more than 25000 per year. If 45% of the company's employees earn more than 25000 per year, what fraction of the women employed by the company earn 25000 per year or less?

(A) 1/4

(B) 3/4

(C) 1/3

(D) 2/11

35. A sum of money invested at compound interest amounts in 3 years to 800 and in 4 years to 840 what is the percentage rate of interest?

(A) 6%

(B) 5%

(C) 4%

(D) 3%

36. If the difference between simple and compound interest on some principal amount at 20% per annum for three years is 48, then the principal amount is:

(A) 390

(B) 375

(C) 450

(D) None of these

37. A rational number between 1/2 and 3/5 is:

(A) 4/7

(B) 3/5

(C) 2/5

(D) None of these

38. The curved surface of a cylinder is 264m². Its volume is 924m³. The height of the cylinder must be:

(A) 8 m

(B) 6 m

(C) 4 m

(D) None of these

39. If by selling 110 apples, the cost price of 120 apples is realised. The gain % is?

(A) 10 10/11%

(B) 9 1/9%

(C) 11 1/9%

(D) 1 1/11%

40. If 8 men or 12 women can do a piece of work in 25 days, in how many days can the same work be done by 6 men and 11 women?

(A) 15 days

(B) 13 1/2 days

(C) 12 days

(D) 18 days

41. Pujara has a certain average of runs for his 8 matches in Border Gavaskar Trophy. In the ninth match he scores 100 runs and thereby increases his average by 9 runs. His new average of runs is:

(A) 28

(B) 24

(C) 20

(D) 32

42. It costs 1 to photocopy a sheet of paper. However, 2% discount is allowed on all photocopies done after first 1000 sheets. How much will it cost to photocopy 5000 sheets of paper?

(A) 3920

(B) 4900

(C) 4920

(D) 3980

DIRECTIONS (Question No 43 & 44) Answer the following questions on the basis of the information given below.

i. Trains A and B are travelling on the same route heading towards the same destination. Train B has already covered a distance of 220km before the train A started.

ii. The two trains meet each other after 11 hours after start of train A

iii. Had the trains been travelling towards each other (from a distance of 220 km) they would have met after one hour.

43. What is the speed of trains 'B' in kmph:

(A) 116

(B) 180

(C) 100

(D) None of these

44. What is the speed of trains 'A' in kmph:

(A) 118

(B) 80.5

(C) 102

(D) None of these

DIRECTIONS: What approximate (you are not expected to calculate the exact value) value will come in place of the question mark(?) in following equation?

45. 384.996 x 15.001 + 44.99 = ?

(A) 5080

(B) 5820

(C) 5280

(D) 5420

46. Three men or eight boys can do a piece of work in 17 days. How many days will two men and six boys together take to finish the same work?

(A) 12 days

(B) 17 days

(C) 11 days

(D) None of these

47. Vaibhav got a monthly increment of 12 percent of Pushpa's monthly salary. Pushpa's monthly salary is 7800. Vaibhav's monthly salary before increment was 6500. What amount will he earn in five months after his increment?

(A) 37.180

(B) 35.180

(C) 36.180

(D) None of these

48. The ratio of two numbers is 4:5. When the first is increased by 20% and the second is decreased by 20% the ratio of the resulting numbers is:

(A) 5:6

(B) 5:4

(C) 6:5

(D) 4:5

49. If the numerator of a fraction be increased by 12% and its denominator decreased by 2% the value of the fraction becomes 6/7. Thus, the original fraction is:

(A) 3/4

(B) 4/3

(C) 2/3

(D) None of these

50. What approximate value will come in place of the question mark (?) in the following equation?

239.99 / 8.0001 x 9.99 = ?

(A) 350

(B) 260

(C) 400

(D) 300