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A total of 324 notes comprising of Rs. 20 and Rs. 50 denominations make a sum of Rs. 12450. The number of Rs. 20 notes is
- a)200
- b)144
- c)125
- d)110
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A total of 324 notes comprising of Rs. 20 and Rs. 50 denominations mak...
Given:
Total number of notes of Rs. 20 and Rs. 50 = 324
Total Sum = Rs. 12450
Concept used:
Value of note × Number of total notes = Total amount
Calculation:
Let the number of Rs. 20 notes be x.
No. of Rs. 50 notes = 324 – x
⇒ 20 × x + 50 × (324 – x) = 12450
⇒ 20x + 16200 – 50x = 12450
⇒ -30x = 12450 – 16200
⇒ 30x = 3750
⇒ x = 125
∴ The number of Rs. 20 notes is 125.
Most Upvoted Answer
A total of 324 notes comprising of Rs. 20 and Rs. 50 denominations mak...
Total Notes and Their Value
To solve the problem, we need to set up a system of equations based on the given information about the notes.
Given Data
- Total number of notes = 324
- Total amount = Rs. 12450
- Denominations = Rs. 20 and Rs. 50
Let’s Define Variables
- Let x = number of Rs. 20 notes
- Let y = number of Rs. 50 notes
Setting Up Equations
1. From the total number of notes:
- x + y = 324
2. From the total value of the notes:
- 20x + 50y = 12450
Simplifying the Equations
- From the first equation, we can express y in terms of x:
- y = 324 - x
- Now substitute y in the second equation:
- 20x + 50(324 - x) = 12450
Expanding and Simplifying
- Distributing the 50:
- 20x + 16200 - 50x = 12450
- Combining like terms:
- -30x + 16200 = 12450
- Rearranging gives:
- -30x = 12450 - 16200
- -30x = -3750
- Dividing both sides by -30 results in:
- x = 125
Conclusion
The number of Rs. 20 notes is 125, which corresponds to option 'C'.
Verification
- If x = 125, then:
- y = 324 - 125 = 199
- Checking the total value:
- Total value = 20(125) + 50(199) = 2500 + 9950 = 12450, which is correct.
Thus, the answer is confirmed!
To solve the problem, we need to set up a system of equations based on the given information about the notes.
Given Data
- Total number of notes = 324
- Total amount = Rs. 12450
- Denominations = Rs. 20 and Rs. 50
Let’s Define Variables
- Let x = number of Rs. 20 notes
- Let y = number of Rs. 50 notes
Setting Up Equations
1. From the total number of notes:
- x + y = 324
2. From the total value of the notes:
- 20x + 50y = 12450
Simplifying the Equations
- From the first equation, we can express y in terms of x:
- y = 324 - x
- Now substitute y in the second equation:
- 20x + 50(324 - x) = 12450
Expanding and Simplifying
- Distributing the 50:
- 20x + 16200 - 50x = 12450
- Combining like terms:
- -30x + 16200 = 12450
- Rearranging gives:
- -30x = 12450 - 16200
- -30x = -3750
- Dividing both sides by -30 results in:
- x = 125
Conclusion
The number of Rs. 20 notes is 125, which corresponds to option 'C'.
Verification
- If x = 125, then:
- y = 324 - 125 = 199
- Checking the total value:
- Total value = 20(125) + 50(199) = 2500 + 9950 = 12450, which is correct.
Thus, the answer is confirmed!
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Community Answer
A total of 324 notes comprising of Rs. 20 and Rs. 50 denominations mak...
Given:
Total number of notes of Rs. 20 and Rs. 50 = 324
Total Sum = Rs. 12450
Concept used:
Value of note × Number of total notes = Total amount
Calculation:
Let the number of Rs. 20 notes be x.
No. of Rs. 50 notes = 324 – x
⇒ 20 × x + 50 × (324 – x) = 12450
⇒ 20x + 16200 – 50x = 12450
⇒ -30x = 12450 – 16200
⇒ 30x = 3750
⇒ x = 125
∴ The number of Rs. 20 notes is 125.
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Question Description
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