Model Aptitude questions and answers for placement - Set 6

1)   Four friends (A, B, C and D) started a business in partnership by investing capitals in the proportion 3 : 5 : 4 : 6. During the period of one-year, these capitals were utilized in the proportion of 6 : 4 : 5 : 3 respectively. If, at the end of the year, a profit of Rs. 15,550 was made, what will be the share of D?

a. Rs. 3250.5
b. Rs. 3750
c. Rs. 4062.59
d. Rs. 3682.89
e. None of these
 Answer  Explanation ANSWER: Rs. 3682.89 Explanation: A = (Investment * capital utilized) = (3 * 6) = 18B = (5 * 4) = 20C = (4 * 5) = 20D = (6 * 3) = 18 Thus, out of Rs. 76 (18 +20 + 20 + 18), D's share is Rs. 18. Hence, out of Rs. 15,500 the share of D would be given as (18/76) * 15550 = Rs. 3682.89

2)   The value of “A” varies in inverse proportion as the square of “B”. If the value of “A” is equal to 40 when “B” is equal to 12. What would be the value of “A” when “B” is equal to 24 ?

a. 10
b. 15
c. 20
d. 22
e. None of these
 Answer  Explanation ANSWER: 10 Explanation: We have, A α 1/B2A * B2 = K (constant)When B = 12, A = 40 …..GivenK = 40 * (12)2 = 5760Now, B = 24. Hence, A = 5760 / 576 = 10

3)   A boy has to cover a total distance of 300 kms. in 6 hours. He travels at the rate of 60 kmph. for first 90 minutes and next 100 kms. at the rate of 50 kmph. At what average speed must he travel now in order to complete the journey in 6 hours?

a. 25 kmph.
b. 32 kmph
c. 44 kmph
d. 58 kmph
 Answer  Explanation ANSWER: 44 kmph Explanation: The boy travels 60 kmph for 90 min, this means he travels 90 km.Next 100 km at the rate of 50 kmph, this means he travels 100 km.Total distance traveled till now = 100 + 90 = 190 kmTime spent = 1.5 + 2 = 3.5 hrRequired speed = Remaining distance/ Time= (300 – 190) /(6 – 3.5)= 110/ 2.5 = 44 kmph

4)   A certain sum earns simple interest of Rs. 800 in 2 years at a certain rate of interest. If the same sum earns compound interest of Rs. 845 in the same period of 2 years, What must be the rate of interest?

a. 5% p.a.
b. 7.5% p.a.
c. 10% p.a.
d. 12.5% p.a.
 Answer  Explanation ANSWER: 10% p.a. Explanation: Given: 800 = (P * R * 2) / 100S.I. For 1 year = Rs. 400Thus, (840 – 800) = S.I. on Rs. 400 for 1 year40 = (400 * R * 1) / 100R = 10% p.a.

5)   An amount of Rs.20,000 is to be distributed amongst P, Q, R and S such that “P” gets twice as that of “Q” and “S” gets four times as that of “R”. If “Q” and “R” are to receive equal amount, what is the difference between the amounts received by S and P?

a. Rs. 5000
b. Rs. 4570
c. Rs. 2750
d. Rs. 2950
 Answer  Explanation ANSWER: Rs. 5000 Explanation: We have, P = 2Q & S = 4RFurther Q = R & P + Q + R + S = 20,000Thus we get, 2Q + Q + Q + 4Q = 20,0008Q = 20,000 or Q = Rs. 2500Thus, R = Rs. 2500, P = 5000 & S = Rs. 10000Hence, the required difference = (S – P) = (10000 – 5000) = Rs. 5000

6)   In the quadratic equation ax2 - 11x + 40 = 0, if the sum of two roots is 1.1, what is the product of the two roots?

a. 4
b. 4.2
c. 8
d. None of these
 Answer  Explanation ANSWER: 4 Explanation: The sum of the roots of the quadratic equation ax2 - bx + c = 0 are (-b/a) and the product of the roots are (c/a).Thus, in the equation ax2 - 11x + 40 = 0, where a = a, b = - 11 and c = 40.we get, sum of the roots = - (- 11) / a = 1.1a = 11 / 1.1 = 10Product of the roots = 40 / 10 = 4

7)   For arranging a picnic, each student contributed an amount equal to the number of students while the teacher contributed an amount equal to twice the number of students. However, if each student would have contributed an amount equal to twice the number of students and the teacher would have contributed an amount equal to the number of students, they would have generated Rs. 1056 more. Find the number of students in the group?

a. 24
b. 25
c. 33
d. 50
e. Cannot be determined
 Answer  Explanation ANSWER: 33 Explanation: Let the number of students = x. Thus, we get,[(2x2 + x) – (x2 + 2x)] = 1056x2 - x - 1056 = 0Solving the equation, we get, x = 33 or x = - 32.Since the number of students are to be positive, number of students = x = 33

8)   By giving Rs. 50 to M, A would have the amount equal to what M had earlier. If the sum of the amounts with A and M is Rs. 650. What is the ratio of the amount with A to that with M earlier?

a. 7 : 4
b. 5 : 3
c. 2 : 1
d. 7 : 6
e. 2 : 3
 Answer  Explanation ANSWER: 7 : 6 Explanation: Let the amounts with A and M be Rs. “X” and Rs. “Y” respectively.Thus, we have, X + Y = 650 andX – 50 = YX – Y = 50.Hence, X = 350 & Y = 300Thus the required ratio is 350 : 300 = 7 : 6

9)   Two-third of two-fifth of three-fourth of a number is 36. What is the square root of four-fifth of that number?

a. 9
b. 12
c. 14
d. 16
e. None of these
 Answer  Explanation ANSWER: 12 Explanation: We have, 2/3 * 2/5 * 3/4 * X = 36X = 180Now, 4/5 * X = 4/5 * 180 = 144√144 = 12

10)   The length and breadth of a rectangular floor are 16.25 metre and 12.75 metre respectively. Find how many minimum number of square tiles would be required to cover it completely?

a. 375
b. 2570
c. 2800
d. 3315
e. None of these
 Answer  Explanation ANSWER: 3315 Explanation: Since we require minimum number of square tiles, the size of the tile is given as the H.C.F. of two sides of the room. The H.C.F. Of 1625 cm & 1275 cm. is 25 cms. Hence, we get,Required Number = (1625 * 1275) / (25 * 25) = 3315