Arithmetic Questions

Joe and Jeff are partners in a business. Joe is an active partner and Jeff is a sleeping one. Joe invests \ 5000$andJeffinvests$ \$6000$. Joe receives $12.5\%$ ($25/2\%$) of the profit for managing the business and the rest is divided in proportion to their investment. What does each get out of a profit of \ 880$?

In a race of $200\text{m}$, $A$ beats $B$ by $45\text{m}$ or $9$ seconds. Find the time taken by $A$ to complete the race.

$300\text{gm}$ of sugar solution has $40\%$ sugar. How much sugar should be added to make it $50\%$ in the solution?

When $67$ is divided by a number $x$, a remainder of $3$ is obtained. If $x<50$, then the largest value of $x$ is:

$A$ can row $15\text{km/h}$ in still water. It takes him twice as long to row upstream as to row downstream. Find the rate downstream.

A solution of $100\text{L}$ contains $75\%$ water and the rest liquid sugar. How much liquid sugar must be added to make it a $50\%$ sugar solution?

A boat takes 2 hours to go 16 km downstream; while covering the same distance upstream, it takes 4 hours. What is the speed of the current?

In a $500\text{m}$ race, the ratio of the speeds of $P$ and $Q$ is $3:4$. When the race starts, $P$ is $140\text{m}$ ahead. What is the distance between $P$ and $Q$ when $P$ wins the race?

A tap can fill a tank in 8 hrs. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?