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प्रश्न
The total cost of 8 books and 5 pens is 420 rupees and the total cost of 5 books and 8 pens is 321 rupees. Find the cost of 1 book and 2 pens.
उत्तर
Let the cost of 1 book be x and the cost of 1 pen be y.
According to the first condition, the total cost of 8 books and 5 pens is 420 rupees.
∴ 8x + 5y = 420 ...(I)
According to the Second condition, the total cost of 5 books and 8 pens is 321 rupees.
5x + 8y = 321 ...(II)
Multiplying equation (I) by 5
40x + 25y = 2100 ...(III)
Multiplying equation (II) by 8
40x + 64y = 2568 ...(IV)
equation (IV) - (III)
40x + 64y = 2568
- 40x + 25y = 2100
39y = 468
∴ y = `468/39`
∴ y = 12
Putting the value of y = 12 in equation (I)
8x + 5y = 420
⇒ 8x + 5 (12) = 420
⇒ 8x + 60 = 420
⇒ 8x = 420 - 60
⇒ 8x = 360
⇒ x = `360/8`
∴ x = 45
Cost of 1 book and 2 pens = x + 2y
= 45 + 2 (12)
= Rs. 69
∴ The Cost of 1 book and 2 pens = Rs. 69.
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