Find the number which, when multiplied by 15, gives a result that is 196 greater than the original number itself.

Introduction:
This is a simple linear equation problem involving one unknown number. The statement says that when the number is multiplied by 15, the resulting product is greater than the original number by 196. This kind of question is very common in aptitude tests and helps reinforce algebraic modeling of verbal descriptions using one equation in one variable.

Given Data / Assumptions:

• Let the original number be x.
• When multiplied by 15, the result is 15x.
• This product is 196 more than the original number, so 15x = x + 196.
• We must solve for x.

Concept / Approach:
Translate the English sentence into an algebraic equation. The phrase “is increased by 196” means “is equal to the original plus 196.” Once the equation 15x = x + 196 is written, it is a straightforward linear equation that can be solved by isolating x on one side.

Step-by-Step Solution:
Let x be the original number.Given: 15x is 196 more than x.So, 15x = x + 196.Subtract x from both sides: 15x - x = 196.14x = 196.x = 196 / 14 = 14.Therefore, the required number is 14.

Verification / Alternative check:
Check the condition using x = 14: 15 * 14 = 210. The original number is 14. The increase is 210 - 14 = 196, which matches the problem statement exactly. Thus x = 14 is correct.

Why Other Options Are Wrong:
10: gives 15 * 10 = 150, increase of only 140.12: gives 15 * 12 = 180, increase of 168.16: gives 240, increase of 224.18: gives 270, increase of 252. None of these equal an increase of 196.

Common Pitfalls:
Misinterpreting the phrase “is increased by 196” as 15x = 196x or 15x + 196 incorrectly.Forgetting to subtract x from both sides when solving 15x = x + 196.Doing division 196/14 incorrectly due to a calculation slip.

Final Answer:
14