Arun Sharma Solutions for Exercise 3: Level of Difficulty

In the mock CAT paper at Mindworkzz, questions were asked in five sections. Out of the total students, $5\%$ candidates cleared the cut-off in all sections, and $5\%$ cleared none. Of the rest, $25\%$ cleared only one section and $20\%$ cleared four sections. If $24.5\%$ of the entire candidates cleared two sections and $300$ candidates cleared three sections, find out how many candidates appeared at the mock CAT at Mindworkzz?

There are three galleries in a coal mine. On the first day, two galleries are operative and after some time, the third gallery is made operative. With this, the output of the mine became half as large again. What is the capacity of the second gallery as a percentage of the first, if it is given that a four-month output of the first and the third galleries was the same as the annual output of the second gallery?

$10\%$ of the salty sea-water contained in a flask was poured out into a beaker. After this, a part of the water contained in the beaker was vaporised by heating and due to this, the percentage of salt in the beaker increased by $M$ times. If it is known that after the content of the beaker was poured into the flask, the percentage of salt in the flask increased by $x\%$, find the original quantity of salty sea-water in the flask.

In an election of three candidates, A, B and C, A gets $50\%$ more votes than B and also beats C by $18000$ votes. If it is known that B gets $5$ percentage point more votes than C, then, find the number of voters on the voting list, such that $90\%$ of the voters on the voting list voted and no votes were illegal.

A clock is set right at $12$ Noon on Monday. It loses $\left(\frac{1}{2}\right)\%$ of the correct time in the first week but gains $\left(\frac{1}{4}\right)\%$ of the true time during the second week. The time shown on Monday after two weeks will be _____.

Abhimanyu Banerjee has $72\%$ vision in his left eye and $68\%$ vision in his right eye. For corrective therapy, he starts wearing contact lenses, which augment his vision by $15\%$ in the left eye and $11\%$ in the right eye. Find the percentage of the normal vision he possesses after corrective therapy. (Assume that a person's eyesight is a multiplicative construct of the eyesight's of his left and right eyes).

Krishna Iyer, a motorist uses $24\%$ of his fuel in covering the first $20\%$ of his total journey (in city driving conditions). If he knows that he has to cover another $25\%$ of his total journey in city driving conditions, approximately what should be the minimum percentage increase in the fuel efficiency for non-city driving over the city driving fuel efficiency, so that he is just able to cover his entire journey without having to refuel?

Harsh Sharma has a salary of $₹10800$ per month. In the first month of the year, he spends $40\%$ of his income on food, $50\%$ on clothing and saves $11.11\%$ of what he has spent. In the next two months, he saves $9.09\%$ of what he has spent (spending $38.33\%$ of his income on food). In the fourth month, he gets an increment of $11.11\%$ on his salary and spends every single paise on celebrating his raise. But from the fifth month onwards, good sense prevails on him and he saves $12.5\%, 15\%, 20\%, 10\%, 8.33\%, 12.5\%, 15\%, 20\%$ on his new income per month. The ratio between the sum of the savings for the two months having the highest savings to the sum of the savings for the two months having the lowest savings is _____.