# ITTIAM

Aptitude Paper:

The speed of a car uphill is 56 mph, speed downhill 72 mph, speed in level ground 63 mph. The time taken to travel from Town A to Town B is 4hrs, and back from Town B to Town A is 4 hours 40 minutes. What is the distance between A and B?

1. One person has n coins and another has (n+1) coins. Both of them toss all of their coins simultaneously. What is the probability that the person having (n+1) coins gets more heads than the other person?
2. Only one of the following said the truth. Who was it?

A: “B did it.”

B: “D did it.”

C: “I didn’t do it.”

D: “B lied.”

1. 6249*p + 3751*q = 26249

3751*p + 6249*q = 237251

What is the value of p? (They gave options as range of value for p)

1. If two numbers are chosen from (1,2,….25) what is the probability that one of the numbers is twice greater than the other number?
2. A man runs 7 steps in an escalator and he reaches the top in 37.5 secs. He runs 13 steps and reaches the top in 22.5 secs. What is the time taken if he does not move while on the escalator (only the escalator moves)?
3. A number is of the form : “abcdefhij”

A denotes the number of 0’s

B denotes the number of 1’s

C denotes the number of 2’s

D denotes the number of 3’s

E denotes the number of 4’s

F denotes the number of 5’s

G denotes the number of 6’s

H denotes the number of 7’s

I denotes the number of 8’s

J denotes the number of 9’s

What is the sum of the digits of the number?

There are 5 brothers A,B,C,D,E. Two of whom are twins. E is younger than B but older than C. And none of the twins are the youngest or oldest. D has three elder bothers.who are the Twins?

1. Who is the eldest?
2. Who is the youngest?
3. A circle of radius r1 revolves around a circle of radius r2()r1<r2) in such a way that the two circles touch at one point externally. What is the number of rotations of r1?
4.   An equlateral triangle and its circumcircle..what is the probability that a line drawn inside this circle is longer than the side of the equilateral triangle        ans =1/3(?)
1. The city B is 1km North and I km east of A. Another city C is 8km east of B. If a line is drawn such that the triangle formed by connecting the 3 cities is divided into 2 equal areas, what is the distance from B of the point at which this line cuts the line BC?
2. A chess board has 8*8 squares. Find the total number of squares in the chess board.
3.  Two numbers m and n are chosen from {1,2,…100}. What is the probability that the number 7^m+7^n is divisible by 5?
4.  ½ is written in the form 1/a+1/b where a and b are two distinct positive integers. Find the minimum value of a^2+b^2.
5. In an army parade, the length of a platoon of soldiers is 50 m. One soldier in the last row runs up to the soldier in the first row, conveys some message and then runs back at the same speed to his position. If the platoon is moving at an uniform speed, what is the distance the soldier has traveled? (75,75+75sqrt(2),75+75sqrt(3),100)
6. How many distinct weights can be measured if one weight of each (1kg, 3kg, 9kg, and 27kg) is given?
7. An ant has to go from one corner(in the inside) of a cube(1m*1m*1m) to the diagonally opposite corner. What is the minimum distance it has to travel?
8. A family goes for a vacation to a place A. in A it so happens that if it rains in the morning, it is clear in the afternoon. The family spent 13 clear mornings and 12 clear afternoons. How many days did the family spend in A?