Find the number such that when it is multiplied by 15, the result is greater than the original number by 56.

Introduction / Context:
This question is a simple algebraic equation problem involving an unknown number and a relationship between its multiple and itself. The statement describes how much bigger the product of the number and 15 is compared to the original number. From this, we can form a linear equation and solve for the unknown. Such questions are meant to test basic equation setup skills in aptitude exams.

Given Data / Assumptions:

• Let the unknown number be x.
• When x is multiplied by 15, the result is 56 more than x.
• We need to determine the value of x.

Concept / Approach:
The phrase "when it is multiplied by 15, the result is 56 greater than the original number" can be expressed algebraically as 15x = x + 56. This is a simple one-variable linear equation. Solving this equation will give the value of x directly. Once x is found, we check whether it matches one of the options and whether it satisfies the original condition stated in the problem.

Step-by-Step Solution:
Step 1: Let the required number be x. Step 2: According to the problem, when x is multiplied by 15, we get a value that is 56 more than x. Step 3: Translate this into an equation: 15x = x + 56. Step 4: Subtract x from both sides to gather like terms: 15x − x = 56. Step 5: This simplifies to 14x = 56. Step 6: Divide both sides by 14: x = 56 / 14. Step 7: Compute the division: 56 / 14 = 4. Step 8: Therefore, the required number is 4.

Verification / Alternative check:
Check the condition with x = 4. The product when multiplied by 15 is 15 * 4 = 60. The original number is 4. The difference 60 − 4 = 56, which matches the statement that the product is 56 greater than the original number. This confirms that x = 4 is correct.

Why Other Options Are Wrong:
Option (a) 6: If x = 6, then 15x = 90 and 90 − 6 = 84, not 56.
Option (c) 3: If x = 3, then 15x = 45 and 45 − 3 = 42, not 56.
Option (d) 12: If x = 12, then 15x = 180 and 180 − 12 = 168, not 56.

Common Pitfalls:
Some learners misinterpret the phrase and write 15x + 56 = x or x = 15x + 56, which reverses or distorts the relationship. Others may make arithmetic errors when subtracting x from 15x. Carefully translating the wording into a correct equation and handling the subtraction correctly avoids these mistakes.

Final Answer:
The required number is 4.