## In a class, if 6 students per bench are assigned to accommodate all students, one more bench will be required. If 7 students are to accommodate per bench, there would be a space left for 5 students. What is the number of students in the class?

Let no. of benches = x (6x+6) =(7x-5) 6+5 = 7x-x x=11. No.of students = (11×6 )+6 =72. With 6 students on the available 11 benches , 66 students will be seated & 1 more bench will be required for the remaining 6. If 7 students are seated on the available 11 benches , 77students …

## N number of persons decided to raise Rs 3 lakhs by equal contributions from each. Had they contributed Rs 50 each extra, the contribution would have been Rs 3.25 lakhs. How many persons are there?

Let the number of persons be ‘n’ and the equal contribution made by each person be ‘x’. Then, the total amount raised by the ‘n’ persons is given by: Total amount = n * x As per the given information, we have two equations: Equation 1: n * x = 3 lakhs Equation 2: (n …

## The price of sugar is increased by 20%. By what percent must the consumption of sugar be decreased so that the expenditure on sugar may remain the same (upto the nearest integer)?

Let’s assume the initial price of sugar was $1$ unit (for simplicity), and the initial consumption was $x$ units, resulting in an expenditure of $1 \times x = x$ units. After the price increase of 20%, the new price of sugar becomes $1+0.2=1.2$ units. To keep the expenditure on sugar the same, we need to …

## A’s income is 25% more than B’s income B’s income in terms of A’s income is

Let’s say that B’s income is x. Then, according to the problem, A’s income is 25% more than B’s income, which means A’s income is: x + 0.25x = 1.25x In terms of A’s income, B’s income is the ratio of B’s income to A’s income, which is: x / (1.25x) = 0.8 Therefore, B’s …

## In an election between two candidates, one got 55% of the total valid votes. 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was

If 20% of the votes were invalid, then 100% – 20% = 80% of the votes were valid. The total number of valid votes is therefore 80/100 * 7500 = 6000. If one candidate got 55% of the valid votes, then the other candidate got 45% of the valid votes. The number of valid votes …

## If two planes leave the same airport at 1:00 PM, how many miles apart will they be at 3:00 PM if one travels directly north at 150 mph and the other travels directly west at 200 mph?

N ^ | | | Plane 1 | Plane 2 (150 mph) | (200 mph) W<———O———>E | | | | S Let’s assume that the planes are at the same airport (point O) at 1:00 PM, and we want to find the distance between them at 3:00 PM (2 hours later). Plane 1 is traveling …

## If Sam can do a job in 4 days that Lisa can do in 6 days and Tom can do in 2 days, how long would the job take if Sam, Liza and Tom work together to complete it?

Let’s first calculate the amount of work each person can do in one day: Sam can do 1/4 of the job in one day (since he can complete the whole job in 4 days). Lisa can do 1/6 of the job in one day (since she can complete the whole job in 6 days). Tom …

## A car travels at the speed of 36 km per hour. What is the distance traveled by the car within 20 second in meter?

First, we need to convert the speed of the car from km/h to m/s since the time is given in seconds. 1 km/h = 1000 m/3600 s = 0.2778 m/s So, the speed of the car is: 36 km/h = 36 x 0.2778 m/s = 10 m/s Now, we can use the formula: distance = …

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