iGATE - Aptitude

iGATE - Aptitude

1.      The average age of a class of 30 students is 12. If the teacher is also included the average becomes 13 years. Find the teacher’s age.
Ans: 43 years

The total age of the 30 students -> 12 x 30 = 360

He average increases by 1, when the age of the teacher is included.

The total age of the students and the teacher -> 13 x 31 = 403

Hence the teacher’s age is 403 – 360 = 43 years.

2.       The average of 13 papers is 40. The average of the first 7 papers is 42 and of the last seven papers is 35. Find the marks obtained in the 7th paper?
(a) 23                     (b) 38                    (c) 19                     (d) None of these

Ans: (c)

The total of 13 papers -> 13 x 40 = 520.

The total of the first 7 papers -> 42 x 7 = 294

The total of the last 7 papers ->  35 x 7 = 245

Total of first 7 and last 7 papers -> 294 + 245 = 539 The 7^th paper which is the middle one among the total 13 is included in both the totals.

Hence the marks obtained in the 7^th paper -> 539 – 520 = 19

3.       The average age of the Indian cricket team playing the Nagpur test is 30. The average age of 5 of the players is 27 and that of another set of 5 players, totally different from the first five, is 29. If it is the captain who was not included in either of these two groups, then find the age of the captain.
(a) 75                     (b) 55                    (c) 50                     (d) Cannot be determined

Ans: (c)

As there are 11 players in the team the total age of the team is 30 x 11 = 330.

The total age of the 5 players is 27 x 5 = 135.

The total age of the different 5 players is 29 x 5 = 145.

Thus the total age of the 10 players is 135 + 145 = 280.

Hence the age of the Captain is 330 – 280 = 50

4.       A bus goes to Ranchi from Patna at the rate of 60 km per hour. Another bus leaves Ranchi for Patna at the same times as the first bus at the rate of 70 km per hour. Find the average speed for the journeys of the two buses combined if it is known that the distance from Ranchi to Patna is 420 kilometers.
(a) 64.615 kmph                (b) 64.5 kmph    (c) 63.823 kmph                (d) 64.82 kmph

Ans: (a)

The distance between Patna and Ranchi is 420 km.

The first bus moving at a speed of 60 kmph would take 7 hours to cover the distance.

The second bus moving at a speed of 70 kmph will take 6 hours to cover the distance.

Thus the average time taken by the two buses together to cover the distance of 420 km is

(6 + 7) / 2 = 6.5 hrs.

Hence the average speed when both the buses are combined is 420/6.5 = 64.615 kmph.

5.       A train travels 8 km in the first quarter of an hour, 6 km in the second quarter and 40 km in the third quarter. Find the average speed of the train per hour over the entire journey.
(a) 72 km/h         (b) 18 km/h        (c) 77.33 km/h   (d) 78.5 km/h
Ans: (b)

The total distance travelled by the train in ¾ hour is 8 + 6 +40 = 54 km

Since the train covers a distance of 54 km in ¾ hour, in one hour it would cover 54 x 4/3 = 72 km.

As the distance covered by the train in each segment is given as quarter of an hour, the average speed of the train for the entire journey is 72/4(quarters) = 18 kmph.

6.       The average weight of 6 men is 68.5 kg. If it is known that Ram and Shyam weigh 60 kg each, find the average weight of the others.
(a) 72.75 kg         (b) 75 kg               (c) 78 kg               (d) None of these

Ans: (a)

The total weight of the 6 men is 68.5 x 6 = 411 kg.

The total weight of Ram & Shyam = 60 + 60 = 120 kg.

Excluding this from the total weight -> 411 – 120 = 291 kg the total weight of the remaining 4 men.

Hence the average weight of the remaining 4 men is 291 / 4 = 72.75 kg.

7.       The average score of a class of 40 students is 52. What will be the average score of the rest of the students if the average score of 10 of the students is 61?
(a) 50                     (b) 47                    (c) 48                     (d) 49

Ans: (d)

The total of the 40 students -> 52 x 40 = 2080

The total of 10 students ->  61 x 10 = 610

The total of the remaining 30 students -> 2080 – 610 = 1470

Thus the average of the 30 students -> 1470/30 = 49

8.       The average age of 80 students of IIM, Bangalore of the 1995 batch is 22 years. What will be the new average if we include the 20 faculty members whose average age is 37 years?
(a) 32 years         (b) 24 years        (c) 25 years         (d) None of these

Ans: (c)

The total age of 80 students -> 22 x 80 = 1760

The total age of 20 faculties ->  37 x 20 =  740

Thus the total age of the students and the faculties is 1760 + 740 = 2500 (Total numbers 100)

Hence the new average age of the students and the faculties is -> 2500/100 = 25

9.       Out of the three numbers, the first is twice the second and three times the third. The average of the three numbers is 88. The smallest number is?
(a) 72                     (b) 36                    (c) 42                     (d) 48

Ans: (d)

Since the average is 88 the total of the three Numbers is 88 x 3 = 264

Let ‘x’ be the first number. Then we have an equation  x + (1/2)x + (1/3)x = 264.

Solving we get the value of ‘x’ as 144. The three numbers are 144 + 72 + 48 = 264.

Hence, the smallest number is 48.

10.   The sum of three numbers is 98. If the ratio between the first and second is 2 : 3 and that between the second and the third is 5 : 8, then the second number is?
(a) 30                     (b) 20                    (c) 58                     (d) 48

Ans: (a)

Let the three numbers be A, B and C.

We have the ratio A : B ::  2 : 3  and B : C :: 5 : 8. B is common in both the ratios but with different values. We shall make the value of B the same in both the ratios. This we can do by multiplying the first ratio 5 and the second by 3. This would give the following two ratios

A : B :: 10 : 15 and B : C :: 15 : 24. Combining both we get the ratio A : B : C :: 10 : 15 : 24

Total 49 parts and since A+B+C = 98 each part is 2. Hence the second number ie B is 30.

 
Problems on Percentage

Let N be the whole Number, P the percent and W part of the number.

Then we have the equation P x N = W.  Using this the following questions can be answered  easily.

11.   42 is what percentage of 168?
(a) 20%                 (b)  25%                (c) 30%                                 (d)  40%
Ans: (b)  Use the formula P = W/N

12.   36 is what percentage of 80?
(a) 65%                 (b)  55%                (c)  45%                                (d)  35%

            Ans: (c)

13.   60 Ps. Is what percent of Rs. 24?
(a)  5/2%              (b)  3/2%              (c)  8/9%              (d)  2/9%

Ans: (a) Please note the question is between Paise and Rupees

14.   16 m is what percentage of 8 km?
(a)  13%                                (b)  14%                (c)  2%                   (d)  None

Ans: (d) The right answer is 0.2%

15.   40% of a number, when added to 42, results in the number itself. What is the number?
(a)  60                    (b)  70                   (c)  80                    (d)  90

Ans: (b) Can be answered from the choices.