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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.

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Rs. 100

Rs. 80

Rs. 75

Rs. 69

answer is D.

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Detailed Solution

Let x rupees be the price of one book.
And the cost of 1 pen is y Rupees.
Given that 8 books and 5 pens cost 420 Rupees. So,

8 x + 5 y = 420

x = \frac{420 - 5 y}{8}

…………………… (1)
Also, cost of 5 books and 8 pens is 321 Rupees.

5 x + 8 y = 321

…………………….. (2)
Put the value of x in this equation from equation (1),

5 (\frac{420 - 5 y}{8}) + 8 y = 321

2100 - 25 y + 64 y = 2568

39 y = 468

y = \frac{468}{39}

y = Rs . 12

Put this value in equation (1) as,

x = \frac{420 - 5 (12)}{8}

x = \frac{420 - 60}{8}

x = \frac{360}{8}

x = Rs . 45

So cost of one book and 2 pen,

x + 2 y = 45 + 2 \times 12

x + 2 y = 45 + 24

x + 2 y = Rs . 69

Correct option is 4.

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