Tech Mahindra – Recent Aptitude and Reasoning Questions
1. Consider a group of working men. If 1/10th of the workers are absent then work of each person would be increased by:
Assume there are 10 workers and they do 100 jobs. Each worker does 10 jobs.
When 1/10 of work force leave, the remaining is 9 workers and they will have to now do 100/9 = 11.11 job. The increase in work load for each person now is – 11.11 – 10 = 1.11
Hence the percentage increase in work load is — 11.11%.
2. Consider the following statements:
(I) All members of team A are good tall guys with an average height of 6 feet.
(II) Average height of members of team B is less than that of team A.
Which could be true among the two options given below?
(a) Every member of team B is shorter than each member of team A.
(b) Few members of team B could be over 6 feet.
The average height of team B is less than that of team A which is 6 feet. This does not mean that members of team B are all shorter than members of team A.
It is possible that some members of team B can be more than 6 feet in height though the average of the team is less than 6 feet.
3. John is supposed to walk from his house to park every morning. One morning, he is in real hurry and wants to save at least 1/3rd of the time. By how much percentage he should increase his speed?
Let us assume that John walks 6 km to the park covering in one hour or 60 minutes.
Hence his speed is 6 km/hr
He now wants to cover the distance in 2/3 hour or 40 minutes to save 1/3 of the time.
His new speed will be — 6 / (2/3) Distance/ time gives the speed.
Thus his ne speed will be —- 6 * 3/2 = 9 km/hr.
Thus the increase in speed over the normal speed of 6 km/hr is 3 km/hr or 50%
4. Pointing to the woman in the picture, Govind said, “Her mother has only one grand -child whose mother is my wife”. How is the woman in the picture related to Govind?
(d) data inadequate
5. Anand is the uncle of Bimala who is the daughter of Cauvery and Cauvery is the daughter in law of Palani. How is Anand related to Palani?
(b) son in law
6. Pointing to a man, Lakshmi says, “This man’s son’s sister is my mother-in-law”. How is the Lakshmi’s husband related to the man?
7. A cylinder of diameter 14 and height 7 is converted into a cone of radius 6. Now, what could be the percentage height of the new shape?
Volume of the cylinder should equal volume of the cone.
Volume of the cylinder is: πr2h -> π * 72 * 7 -> 343π ————- (i)
Volume of the cone is : 1/3 (πr2h) -> 1/3 (π * 62 * h) -> 12πh —— (ii)
Since (i) and (ii) are equal we get the value of h as —– h = 343/12
Percentage increase in height ——- [(343/12) – 7] / 7 * 100 = 308% (approx.)
8. Find the largest number which gives out reminders 2 and 5 when used to divide 80 and 122.
(d) infinite number of solutions
Find the HCF of (80 -2) and (122 – 5) -> 78 and 117. HCF is 13 and that’s the answer.
9. Find the ratio of the volumes of a sphere and cone of same radius. Also the height of the cone is twice its radius.
(a) 3 : 1
(b) 4 : 3
(c) 4 : 1
(d) 2 : 1
The volume of a sphere is 4/3 πr3.
Volume of a cone is 1/3 (πr2h). It is given in the question that h is equal to 2r.
Thus we get the volume of the cone as –—- 1/3 ( πr2*2r) -> 2/3πr3
Hence the ratio of volume of sphere and cone ——- 4/3 πr3 / 2/3 πr3 -> 2 : 1
10. Find the missing number in the sequence 504 , _ , 990, 1320, 1716
The series is (n3-n). The first is 83-8, the second is 93-9, the third is 103-10 and so on.
11. The perimeter of a square and a rectangle is the same. If the rectangle is 12 cm by 10 cm, then by what percentage is the area of the square more than that of the rectangle?
Since the sides of the rectangle are 12 cm and 10 cm, its perimeter is – 2*12 + 2*10 = 44 cm
The perimeter of the Square is the same as the rectangle and is — 44 cm
Hence each side of the square is – 44/4 = 11 cm.
The area of the square is — 11*11 = 121 sq.cm.
The area of the rectangle is — 12 * 10 = 120 sq.com
Thus the Area of the square is 1 cm more than the area of the rectangle.
The percentage increase in the area —— 1/120 * 100 = 5/6%
12. Capacity of a cylindrical vessel is 25,872 litres. If the height of the cylinder is 200% more than the radius of its base, what is the area of the base in square cms?
(d) cannot be determined
The volume of the cylinder is — πr2h. Now from the information h = r +(200% of r) = 3r
Thus the volume of the cylinder is — 3πr3 and this is equal to — 25872 litres.
Hence – r3 = 25872/3π -> 25872 / 3*22/7 -> 2744 and r = 14.
Hence the area of the base is —- πr2 -> 22/7 * 14 * 14 = 616 sq.cm
13. If the radius of a circle is increased by 12%, then the area of the circle
(a) decreases by 25.44%
(b) increases by 25.44%
(c) no change in area
(d) decreases by 12%
Ans: (b) (No working is required)
14. Aravamudhan, Balakrishnan and Chinnan work in a developing software company in starting level positions. However their salaries are different. Aravamudhan’s salary to Balakrishnan’s salary and Balakrishnan’s salary to Chinnan’s salary are in the ratio 4:3. If the total salary of all the three employees is Rs.29230, what is the salary of Chinnan?
Ratio of Aravamudhan : Balakrishnan :: 4 : 3
Ratio of Balakrishnan : Chinnan :: 4 : 3
Now assuming Aravamudhan salary as Rs 4, then Balakrishnan’s salary will be Rs 3.
Now Balakrishnan/Chinnan = 4/3 -> 3/Chinnan = 4/3 -> Chinnan salary will be 9/4.
Thus the total salary of all the three is ———- 4 + 3 + 9/4 -> 37/4
We know the total salary is Rs 29230 which is equal to 37/4 (as arrived above)
Chinnan’s salary is 9/4 which is equal to —- 29230 * (9/4)/(37/4) -> Rs 7,110/-
15. Three cricket players — Ramesh, Suresh and Ganesh play for three different cricket Teams – Haryana, Delhi and Rajasthan respectively. Ramesh was born in Chennai but brought up in Karnal, Haryana. Suresh was born in Delhi and brought up in Delhi. Ganesh’s fore-fathers were from Madurai but settled in Rajasthan. All the three participated in a cricket tournament. Ramesh’s runs to Suresh’s runs and Suresh’s runs to Ganesh’s runs are in the ratio 5:7. If the total runs scored by all the three players in the tournament is 327, find the total runs scored by Suresh in the tournament?
This question is similar to the earlier question and we shall proceed from the last ratio:
Suresh : Ganesh :: 5 : 7
Ramesh : Suresh :: 5 : 7
Assuming Ganesh scored 7 runs, then Suresh scored 5 runs.
Now, Ramesh/Suresh :: 5/7 -> 7 Ramesh = 5 x 5 = 25. Hence, Ramesh = 25/7
We know the total runs scored as 327.
Thus we have —– (R) 25/7 + (S) 5 + (G) 7 = 327 -> 109/7 = 327.
Runs scored by Suresh is ——- 327/(109/7) * 5 -> 105.