Interview Q&A / Aptitude

1. How do you calculate successive percentage changes?

   Two changes of a% and b% give a net change of a + b + (a x b) / 100 percent. Use negative values for decreases. For example, a 20% increase followed by a 20% decrease is a net 4% decrease, not zero.

   BeginnerIn-depth3 min read
2. How do you solve profit and loss questions with marked price and discount?

   Profit or loss percent is always calculated on the cost price. Discount percent is always calculated on the marked price. Chain them with multipliers. For example, mark up 25% and give 10% off, and the selling price is 1.25 x 0.9 = 1.125 times the cost, which is a 12.5% profit.

   BeginnerIn-depth4 min read
3. How do you solve ratio and age problems?

   Write the present ages as multiples of one unknown using the given ratio, such as 4x and 5x, then add or subtract the same number of years to both and set up an equation from the second condition. Both people age by the same amount, so the difference between their ages never changes.

   BeginnerIn-depth4 min read
4. How do you solve time and work problems quickly?

   Convert each person's time into work per day (1 divided by days), add rates when people work together, and divide total work by the combined rate. The LCM method makes it faster. Take total work as the LCM of the days, so each rate becomes a whole number.

   BeginnerIn-depth3 min read
5. What is the difference between simple interest and compound interest?

   Simple interest is calculated only on the original principal, so it is the same every year (SI = P x R x T / 100). Compound interest is calculated on the principal plus the interest already earned, so it grows every year (A = P x (1 + R/100)^T). For 2 years, the difference is P x (R/100)^2.

   BeginnerIn-depth4 min read
6. How do you solve probability questions on coins, dice and cards?

   Probability = favourable outcomes / total outcomes, when all outcomes are equally likely. List the sample space carefully. Two coins have 4 outcomes, two dice have 36, a deck has 52 cards. For "at least one" questions, use 1 minus the probability of none.

   IntermediateIn-depth4 min read
7. How do you solve speed, distance and time questions, including trains and relative speed?

   Use distance = speed x time and convert km/h to m/s by multiplying by 5/18. A train crossing a pole covers its own length; crossing a platform or another train covers both lengths. Add speeds when objects move in opposite directions and subtract when they move in the same direction.

   IntermediateIn-depth4 min read
8. What is the difference between permutations and combinations, and how do you know which to use?

   Use permutations when order matters, like choosing a captain and vice-captain, and combinations when order does not matter, like choosing a committee. nPr = n! / (n - r)! and nCr = n! / (r! x (n - r)!). Each combination of r items can be arranged in r! ways, so nPr = nCr x r!.

   AdvancedIn-depth4 min read