CAT1996 Related Question Answers

26. Answer the questions based on the following information. A salesman enters the quantity sold and the price into the computer. Both the numbers are two-digit numbers. But, by mistake, both the numbers were entered with their digits interchanged The total sales value remained the same, i.e. Rs. 1,148, but the inventory increased by 54.What is the actual price per piece?

27. What is the actual quantity sold?

28. In a locality, two-thirds of the people have cable TV, one-fifth have VCR, and one-tenth have both. What is the fraction of people having atleast one among cable -TV and VCR?

29. Find the value of $$\frac{1}{1 + \frac{1}{3-\frac{4}{2+\frac{1}{3-\frac{1}{2}}}}}$$ + $$\frac{3}{3 - \frac{4}{3+\frac{1}{2-\frac{1}{2}}}}$$

30. Given the quadratic equation $$x^2 - (A - 3)x - (A - 2)$$, for what value of $$A$$ will the sum of the squares of the roots be zero?

31. The figure shows the rectangle ABCD with a semicircle and a circle inscribed inside in it as shown. What is the ratio of the area of the circle to that of the semicircle?

32. I bought 5 pens, 7 pencils and 4 erasers. Rajan bought 6 pens, 8 erasers and 14 pencils for an amount which was half more what I had paid. What per cent of the total amount paid by me was paid for the pens?

33. In a mile race, Akshay can be given a start of 128 m by Bhairav. If Bhairav can give Chinmay a start of 4 m in a 100 m dash, then who out of Akshay and Chinmay will win a race of one and half miles, and what will be the final lead given by the winner to the loser? (One mile is 1,600 m.)

34. Two liquids A and B are in the ratio 5 : 1 in container 1 and 1 : 3 in container 2. In what ratio should the contents of the two containers be mixed so as to obtain a mixture of A and B in the ratio 1 : 1?

35. A man travels three-fifths of a distance AB at a speed 3a, and the remaining at a speed 2b.If he goes from B to A and return at a speed 5c in the same time, then

36. A man travels from A to B at a speed x km/hr. He then rests at B for x hours. He then travels from B to C at a speed 2x km/hr and rests for 2x hours. He moves further to D at a speed twice as that between B and C. He thus reaches D in 16 hr. If distances A-B, B-C and C-D are all equal to 12 km, the time for which he rested at B could be

37. Out of two-thirds of the total number of basketball matches, a team has won 17 matches and lost 3 of them. What is the maximum number of matches that the team can lose and still win more than three- fourths of the total number of matches, if it is true that no match can end in a tie?

38. The price of a Maruti car rises by 30% while the sales of the car come down by 20%. What is the percentage change in the total revenue?

39. The points of intersection of three lines $$2x+3y-5=0, 5x-7y+2=0$$ and $$9x-5y-4=0$$

40. A man has 9 friends: 4 boys and 5 girls. In how many ways can he invite them, if there has to be exactly 3 girls in the invitees?

41. In a watch, the minute hand crosses the hour hand for the third time exactly after every 3 hr 18 min and 15s of normal time. What is the time gained or lost by this watch in one day?

42. I sold two watches for Rs. 300 each, one at the loss of 10% and the other at the profit of 10%. What is the percentage of loss(-) or profit(+) that resulted from the transaction?

43. Answer the questions based on the following information. A series $$S_{1}$$ of five positive integers is such that the third term is half the first term and the fifth term is 20 more than the first term. In series $$S_{2}$$, the nth term is defined as the difference between the (n+1)th term and the nth term of series $$S_{1}$$, $$S_{2}$$ is an arithmetic progression with a common difference of 30.First term of $$S_{1}$$ is

44. Fourth term of $$S_{2}$$

45. What is the difference between fourth terms of $$S_{1}$$ and $$S_{2}$$ ?

46. What is the average value of the terms of series $$S_{1}$$?

47. What is the sum of series $$S_{2}$$?

48. Answer the questions based on the following information. The average revenue collected in the given 7 years is approximately

49. Answer the questions based on the following information. The expenditure for the 7 years together form what per cent of the revenues during the same period?

50. Answer the questions based on the following information. Which year showed the greatest percentage increase in profit as compared to the previous year?

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