Quantitative Aptitude

Concept: Profit or gain percentage is calculated using the formula: If the selling price of some articles equals the cost price of a larger number of articles, then the seller is making a profit.
Step 1:Forming the relation from the given condition.
Let the cost price of one article be and the selling price of one article be . Given:
Step 2:Finding the profit per article.

Step 3:Calculating the gain percentage.

Concept: When a train crosses a pole, the distance covered by the train is equal to the length of the train. Time is calculated using the formula: Also, speeds must be in m/s when distance is in meters.
Step 1:Convert the speed from km/hr to m/s.

Step 2:Use the time formula.
Distance covered = length of train = m Thus, the train will take 10 seconds to cross the pole.

Concept: In symbolic operation questions, first replace the symbols with their actual mathematical operations and then solve the expression using the BODMAS rule (Bracket, Order, Division, Multiplication, Addition, Subtraction). Given:
Step 1:Replace the symbols with the corresponding operations.

Step 2:Apply the BODMAS rule (perform multiplication and division first).
So the expression becomes:
Step 3:Perform addition and subtraction.
Thus, the value of the expression is:

Concept: In simple interest, the interest earned is directly proportional to time. If a certain sum doubles in a given time, then the interest earned in that time equals the principal.
Simple Interest formula: Also,
Step 1:Finding the interest earned in 5 years.
If the sum doubles in 5 years, then: Thus, So, in 5 years the interest earned is equal to the principal.
Step 2:Finding the interest required to make the amount four times.
If the money becomes four times: Thus, required interest:
Step 3:Using proportionality of simple interest with time.
If interest in years, Then interest in: Therefore, the money will become four times in 15 years.