IPMAT Indore Algebra > Linear Equation PYQs

The Celsius scale of temperature can be converted to Fahrenheit scale using the relationship $F = 1.8C + 32$, where $F$ and $C$ are temperature recorded in degrees Fahrenheit and Celsius, respectively. Ajay noted down the temperature of a chemical reaction as $x$ degrees Fahrenheit but reported it as $x$ degrees Celsius by mistake. If this led to a recording of the temperature that was 144% higher than the actual temperature in Celsius scale, then $x$ equals ___

Monica, who is 18 years old, is one-third the age of her father. The age at which she will be half the age of her father is ____

A fruit seller had a certain number of apples, bananas, and oranges at the start of the day. The number of bananas was 10 more than the number of apples, and the total number of bananas and apples was a multiple of 11. She was able to sell 70% of the apples, 60% of bananas, and 50% of oranges during the day. If she was able to sell 55% of the fruits she had at the start of the day, then the minimum number of oranges she had at the start of the day was

For some non-zero real values of $a, b$ and $c$, it is given that $\left|\frac{c}{a}\right|=4,\left|\frac{a}{b}\right|=\frac{1}{3}$ and $\frac{b}{c}=-\frac{3}{4}$. If $a c>0$, then $\left(\frac{b+c}{a}\right)$ equals

In an election with only two contesting candidates, 15% of the voters did not turn up to vote and 50 voters cast invalid votes. It is known that 44% of all the voters in the voting list voted for the winner. If the winner got 200 votes more than the other candidate, then the number of voters in the voting list is