i) 5 पेंसिल तथा 7 कलमों का कुल मूल्य ₹ 50 है, जबकि 7 पेंसिल तथा 5 कलमों का
कुल मूल्य ₹ 46 है। एक पेंसिल का मूल्य तथा एक कलम का मूल्य ज्ञात कीजिए।ans
Answers
Given: 5 पेंसिल तथा 7 कलमों का कुल मूल्य ₹ 50 है,
7 पेंसिल तथा 5 कलमों का कुल मूल्य ₹ 46 है
To Find : एक पेंसिल का मूल्य तथा एक कलम का मूल्य
Solution:
एक पेंसिल का मूल्य = ₹ P
एक कलम का मूल्य = ₹ K
5 पेंसिल तथा 7 कलमों का कुल मूल्य ₹ 50 है,
=> 5P + 7K = 50 Eq1
7 पेंसिल तथा 5 कलमों का कुल मूल्य ₹ 46 है
7P + 5K = 46 Eq2
Eq1 + Eq2
=> 12P + 12K = 96
=> P + K = 8 Eq3
Eq1 - Eq2
=> -2P + 2K = 4
=> K - P = 2 Eq4
Eq3 + Eq4
=> 2K = 10
=> K = 5
=> P = 3
एक पेंसिल का मूल्य = ₹ 3 तथा एक कलम का मूल्य ₹ 5
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Given:
5 पेंसिल तथा 7 कलमों का कुल मूल्य ₹ 50 है, जबकि 7 पेंसिल तथा 5 कलमों का
कुल मूल्य ₹ 46 है। एक पेंसिल का मूल्य तथा एक कलम का मूल्य ज्ञात कीजिए।
The total cost of 5 pencils and 7 pens is ₹ 50, while the cost of 7 pencils and 5 pens is ₹ 46. Find the cost of a pencil and the cost of a pen.
To find:
एक पेंसिल का मूल्य तथा एक कलम का मूल्य ज्ञात कीजिए।
Solution:
Let's say,
"x" → represents the cost of 1 pencil
"y" → represents the cost of 1 pen
The total cost of 5 pencils and 7 pens is ₹ 50, so the equation will be:
5x + 7y = 50 . . . (1)
The cost of 7 pencils and 5 pens is ₹ 46, so the equation will be:
7x + 5y = 46 . . . (2)
On multiplying equation (1) by 7 and equation (2) by 5, we get
35x + 49y = 350 . . . (3)
35x + 25y = 230 . . . (4)
On subtracting equation (3) and (4), we get
35x + 49y = 350
35x + 25y = 230
- - -
24y = 120
--------------------------
∴ y = 5
On substituting the value of y = 5 in equation (1), we get
5x + (7 × 5) = 50
⇒ 5x + 35 = 50
⇒ 5x = 15
⇒ x = 3
Thus,
The cost of 1 pencil is → Rs. 3
The cost of 1 pen is → Rs. 5
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