Nishit K Sinha Solutions for Chapter: Miscellaneous, Exercise 3: Practice Exercises

Amitabh makes a road trip to the Hooghly beach. If he averaged his speed $5 \mathrm{kmph}$ more, he could have decreased his time by $10\%$. On the other hand, if he averaged his speed $5 \mathrm{kmph}$ less, the journey to the beach would have taken an extra hour. What is the distance from Amitabh's home to the Hooghly beach?

The length of a ladder exactly equals the height of a wall. If the ladder is placed on a $2\mathrm{ft}$ tall stool placed $10\mathrm{ft}$ away from the wall, then its tip can just touch the top of the wall. The height of the wall is:

A tree of height $21 \mathrm{m}$ on a roadside broke at a certain height and fell in such a way that its top touched the other edge of the road. If the breadth of the road is $12 \mathrm{m}$, then the height above the ground at which the tree broke was:

In a chess tournament, each of the $5$players plays against every other player. No game results in a draw and the winner of each game gets one point and the loser gets zero. Then, which one of the following sequences cannot represent the scores of the five players?

We consider the relation 'a person x shakes hand with a person y '. Obviously, if x shakes hand y, then y shakes hand with x. In a gathering of 99 persons, one of the following statements is always true, considering 0 to be an even number. Which one is it?

Let P, Q, R, S, and T be statements such that if P is true, then both Q and S are true, and if both R and S are true, then T is false. We then have:

If  A, B, C, and D are statements such that if at least one of A and B is true, then at least one of C and D must be true. Further more, both A and C are false. We then have:

If $\mathrm{x}, \mathrm{y},$ and $\mathrm{z}$are eliminated from the equations $\frac{\mathrm{x}}{\mathrm{y}}=\frac{\mathrm{a}+1}{\mathrm{a}-1},\frac{\mathrm{y}}{\mathrm{z}}=\frac{\mathrm{b}+1}{\mathrm{b}-1}$, and, $\frac{\mathrm{z}}{\mathrm{x}}=\frac{\mathrm{c}+1}{\mathrm{c}-1}$, then which of the following is true regarding the relationship between a, b, and c ?