Question

A Lending library has a fixed charge for the first seven days and an additional charge for each day thereafter. Amrita paid & 65 for a book kept for twelve days, while Supriya Baid80 for the book she kept for fifteen days. What charges would one have to pay to keeponthe book for 20 days?

Answer 1

$\large\underline{\sf{Solution-}}$

Let assume that

Fixed charge for the seven days be Rs x

and

Additional Charge per day there after be Rs y

Case :- 1

Amrita paid Rs 65 for a book kept for twelve days.

It means,

Charge for 7 days = Rs x

and

Charge for extra 5 days = Rs 5y

So, Total amount paid = Rs 65

$\red{\rm :\longmapsto\:x + 5y = 65 - - - (1)}$

Case :- 2

Supriya paid Rs 80 for the book, she kept for fifteen days.

It means,

Charge for 7 days = Rs x

and

Charge for extra 8 days = Rs 8y

So, Total amount paid = Rs 80

$\red{\rm :\longmapsto\:x + 8y = 80 - - - (2)}$

On Subtracting equation (1) from equation (2), we get

$\rm :\longmapsto\:3y = 15$

$\rm :\longmapsto\:y = 5 - - - (3)$

On substituting the value of y in equation (1), we get

$\rm :\longmapsto\:x + 5 \times 5 = 65$

$\rm :\longmapsto\:x + 25 = 65$

$\rm :\longmapsto\:x = 65 - 25$

$\rm :\longmapsto\:x = 40$

So,

If book is kept for 20 days.

Fixed charges for 7 days = Rs 40

Additional charge per day there after = Rs 5

So,

Charges for additional 13 days = 13 × 5 = 65

Total amount paid for 20 days = 40 + 65 = Rs 105

Answer 2

Answer:

$\large\underline{\sf{Solution-}}Solution−</p><p></p><p>Let assume that</p><p></p><p>Fixed charge for the seven days be Rs x</p><p></p><p>and</p><p></p><p>Additional Charge per day there after be Rs y</p><p></p><p>Case :- 1</p><p></p><p>Amrita paid Rs 65 for a book kept for twelve days.</p><p></p><p>It means,</p><p></p><p>Charge for 7 days = Rs x</p><p></p><p>and</p><p></p><p>Charge for extra 5 days = Rs 5y</p><p></p><p>So, Total amount paid = Rs 65</p><p></p><p>\red{\rm :\longmapsto\:x + 5y = 65 - - - (1)}:⟼x+5y=65−−−(1)</p><p></p><p>Case :- 2</p><p></p><p>Supriya paid Rs 80 for the book, she kept for fifteen days.</p><p></p><p>It means,</p><p></p><p>Charge for 7 days = Rs x</p><p></p><p>and</p><p></p><p>Charge for extra 8 days = Rs 8y</p><p></p><p>So, Total amount paid = Rs 80</p><p></p><p>\red{\rm :\longmapsto\:x + 8y = 80 - - - (2)}:⟼x+8y=80−−−(2)</p><p></p><p>On Subtracting equation (1) from equation (2), we get</p><p></p><p>\rm :\longmapsto\:3y = 15:⟼3y=15</p><p></p><p>\rm :\longmapsto\:y = 5 - - - (3):⟼y=5−−−(3)</p><p></p><p>On substituting the value of y in equation (1), we get</p><p></p><p>\rm :\longmapsto\:x + 5 \times 5 = 65:⟼x+5×5=65</p><p></p><p>\rm :\longmapsto\:x + 25 = 65:⟼x+25=65</p><p></p><p>\rm :\longmapsto\:x = 65 - 25:⟼x=65−25</p><p></p><p>\rm :\longmapsto\:x = 40:⟼x=40</p><p></p><p>So,</p><p></p><p>If book is kept for 20 days.</p><p></p><p>Fixed charges for 7 days = Rs 40</p><p></p><p>Additional charge per day there after = Rs 5</p><p></p><p>So,</p><p></p><p>Charges for additional 13 days = 13 × 5 = 65</p><p></p><p>Total amount paid for 20 days = 40 + 65 = Rs 105</p><p></p><p>$