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In a bangle shop, if the shopkeeper displays the bangles in the form of a square then he is left with 38 bangles. If he wanted to increase the size of square by one unit each side of the square he found that 25 bangles fall short of in completing the square. The actual number of bangles which he had with him in the shop was ________.
  • a)
    1690
  • b)
    999
  • c)
    538
  • d)
    Can’t be determined
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
In a bangle shop, if the shopkeeper displays the bangles in the form o...
Let the number of bangles in a side of square = x
According to the question, x2 + 38 = Total no. of bangles ...(1)
Also, (x + 1)2 – 25 = Total no. of bangles ...(2)
From (1) and (2), we have
x2 + 38 = (x + 1)2 – 25
⇒ 38 + 24 = 2x ⇒ x = 31
∴ Total no. of bangles = (31)2 + 38 = 999
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Community Answer
In a bangle shop, if the shopkeeper displays the bangles in the form o...
Understanding the Problem
To solve the problem, we need to set up the equations based on the information provided.
Step 1: Define Variables
- Let \( n \) be the number of bangles that can form a complete square.
- Therefore, the total number of bangles can be expressed as \( n^2 + 38 \) (since 38 bangles are left after forming a square).
Step 2: Increase the Square's Size
- When the shopkeeper increases the size of the square by one unit, the new square would have \( (n+1)^2 \) bangles.
- According to the problem, he is short of 25 bangles to complete this new square, so we can write the equation:
\[
n^2 + 38 = (n+1)^2 - 25
\]
Step 3: Simplifying the Equation
- Expanding \( (n+1)^2 \):
\[
(n+1)^2 = n^2 + 2n + 1
\]
- Substitute back into the equation:
\[
n^2 + 38 = n^2 + 2n + 1 - 25
\]
- This simplifies to:
\[
38 = 2n - 24
\]
- Rearranging gives:
\[
2n = 62 \quad \Rightarrow \quad n = 31
\]
Step 4: Calculate Total Bangles
- Now, substituting \( n \) back to find the total number of bangles:
\[
\text{Total bangles} = n^2 + 38 = 31^2 + 38 = 961 + 38 = 999
\]
Conclusion
Thus, the actual number of bangles the shopkeeper had is 999. The correct answer is option 'B'.
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In a bangle shop, if the shopkeeper displays the bangles in the form of a square then he is left with 38 bangles. If he wanted to increase the size of square by one unit each side of the square he found that 25 bangles fall short of in completing the square. The actual number of bangles which he had with him in the shop was ________.a)1690b)999c)538d)Can’t be determinedCorrect answer is option 'B'. Can you explain this answer?
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In a bangle shop, if the shopkeeper displays the bangles in the form of a square then he is left with 38 bangles. If he wanted to increase the size of square by one unit each side of the square he found that 25 bangles fall short of in completing the square. The actual number of bangles which he had with him in the shop was ________.a)1690b)999c)538d)Can’t be determinedCorrect answer is option 'B'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about In a bangle shop, if the shopkeeper displays the bangles in the form of a square then he is left with 38 bangles. If he wanted to increase the size of square by one unit each side of the square he found that 25 bangles fall short of in completing the square. The actual number of bangles which he had with him in the shop was ________.a)1690b)999c)538d)Can’t be determinedCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a bangle shop, if the shopkeeper displays the bangles in the form of a square then he is left with 38 bangles. If he wanted to increase the size of square by one unit each side of the square he found that 25 bangles fall short of in completing the square. The actual number of bangles which he had with him in the shop was ________.a)1690b)999c)538d)Can’t be determinedCorrect answer is option 'B'. Can you explain this answer?.
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