Question

8. A shopkeeper gives books on rent for reading. She takes a fixed charge for the first two days, and an additional charge for each days thereafter. Simona paid Rs 22 for a book kept for six days, while Satwik paid Rs 16 for the book kept for four days. Find the fixed charges and the charge for each extra day.

( Ans : Rs 10, Rs 3 )

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Answer 1

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Difficulty Level : Average

Chances of being asked in Board : 60%

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Let the fixed charge be Rs.x and the extra charge per day by Rs.y

Then

ATQ, CASE 1

=> x + 4y = 22 (2 + 4)

=> x = 22 - 4y ---------(1)

CASE 2

=> x + 2y = 16 (2 + 2)

Substituting 1 in above equation

=> 22 - 4y + 2y = 16

=> 2y = 6

=> y = 3 <<<<< Answer

Using y in (1)

=> x = 22 - 4(3)

=> x = 10 <<<<<<< Answer

Thus the fixed charge is Rs.10 and the extra charge per day is Rs.3

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Answer 2

Simona: 6 days = Rs 22 (Given)

Satwik: 4 days = Rs 16 (GIven)

.

Find the cost of 1 addition day:

Difference in the days between Simona and Satwik = 6 - 4 = 2

Difference in the amount they paid = Rs 22 - Rs 16 = Rs 6

2 days = Rs 6

1 day = 6 ÷ 2

1 day = Rs 3

.

Find the first 2 day fixed cost:

Simona: 6 days = Rs 22 (Given)

Number of additional charge day = 6 - 2 = 4

Total additional charge = 4 x 3 = Rs 12

Fixed charged for the first 2 days = Rs 22 - Rs 12 = Rs 10

.

Answer: The fixed cost for the first 2 days is Rs 10 and each additional day costs Rs 3.