Problems Based on Arithmetics

Solve this:

You have got a compass and straight-edge (un-marked ruler). Each time you use compass (to draw an arc) you have to pay $20$ and for using ruler (to draw line) you have to pay $1$. If you have got $71000$ to spend (on these) what is the maximum number of pairs to perpendicular lines you can construct?

In a flight of $600 \mathrm{km}$, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by $200 \mathrm{km}/\mathrm{hr}$ and the time of flight is increased by $30$ minutes. What is the original duration of the flight.

${\left(\mathrm{p}+\mathrm{q}\right)}^{\mathrm{th}}$ term of an $\mathrm{AP}$ is $\mathrm{m}$ and ${\left(\mathrm{p}-\mathrm{q}\right)}^{\mathrm{th}}$ term is $\mathrm{n}$. Find ${\mathrm{p}}^{\mathrm{th}}$ term.

How many $5$'s are there in the given number sequence each of which are immediately preceded by $3$ or $4$ but are not immediately followed by $8$ or $9$?

$3 5 9 5 4 5 5 3 5 8 4 5 6 7 3 5 7 5 5 4 5 2 3 5 1 0$

The average age of a six-member family is $22$ years. If the youngest member of the family is $7$ years old, then one hour before the birth of this member, what was the average age of the family?

Five persons fire bullets at a target at the interval of $6, 7, 8, 9$ and $12$ seconds respectively. How many times in an hour they would fire the bullets together at the target?

Find the next term of the $\mathrm{AP} \mathbf{:} \sqrt{18}, \sqrt{50}, \sqrt{98}, .....$

Two goods train each $500 \mathrm{m}$ long are running in opposite directions on parallel tracks. Their speeds are $45 \mathrm{km}/\mathrm{hr}$ and $30 \mathrm{km}/\mathrm{hr}$ respectively. Find the time taken by the slower train to pass the driver of the faster one.

Find the sum of the first $12$ terms of an $\mathrm{AP}$ if ${\mathrm{n}}^{\mathrm{th}}$ term is given by ${\mathrm{a}}_{\mathrm{n}}=3\mathrm{n}+4$.

If $20\%$ of $x=y$, then which of the following is same as $y\%$ of $20$.

If Chandra is smaller in height than Rina. Puja is taller than Sita and Sita is taller than Rina. Who among these are smallest in height?

In a cricket season, India defeated Australia twice, West Indies defeated India twice, Australia defeated West Indies twice, India defeated New Zealand twice and West Indies defeated New Zealand twice. Which country has lost the most number of times?

A batsman in his ${18}^{th}$ innings makes a score of $150$ runs and thereby increasing his average by $6$. Find his average after ${18}^{th}$ innings. 

A person decided to go on a weekend trip and decided not to exceed $8$ hours driving in a day. The average speed of the forward journey is $40 m/h$. Due to traffic on Sundays; the return journey average speed is $30 m/h$. How far he can select a picnic spot?

Find the value of $\frac{\left(6^2+7^2+8^2+9^2+{10}^2\right)}{\left(\sqrt{4}+\sqrt{3}\right)\left(\sqrt{4}-\sqrt{3}\right)}$.

Mark at the following information and answer the question based on it. Seven students $J, K, L, M, N, O,$ and $P$ are standing in a row from left to right in random order such that:

$\left(1\right) P, O, K$and $N$ do not stand at either end.

$\left(2\right) M$ is not in the middle

$\left(3\right) J$ stand to the left of $P$ and to the right of $O$

$\left(4\right) K$ stands on the right side of $N$ and on the left side of $L$

$K$ travels a certain distance with $L$ at a speed of $3 km./hour.$ He then completes a total of $27km$ with $M$at a speed of $6 km/hour$ in $7 hours.$

What is the least number of coins required to make one rupee from different coins of $1, 5, 10$ and $25 \mathrm{paise}$  so that you have at least one coin of each type

Find the value:

$\sqrt{10+\sqrt{25+\sqrt{108+\sqrt{154+\sqrt{225}}}}}$

If $2\times 2=16, 2\times 3=36, 2\times 4=64$ then $2\times 6=$?