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

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A shopkeeper gives books on rent for reading. She takes a fixed charge for the first two days and an additional charge for each day thereafter.

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asked Feb 9, 2018 in Class X Maths by akansha Expert (2.2k points)

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

pair of linear equations in two variables

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answered Feb 9, 2018 by aditya23 (-2,146 points)

Let Latika takes a fixed charge for the first two day is ₹ x and additional charge for each day thereafter is ₹ y.

Now by first condition.

Latika paid ₹ 22 for a book kept for six days i.e.,

x + 4 y = 22 …(i)

and by second condition,

Anand paid ₹ 16 for a book kept for four days i.e.,

x+2y=16 …(ii)

Now, subtracting Eq. (ii) from Eq. (i), we get

2y=6⇒ y = 3

On putting the value of y in Eq. (ii), we get

x + 2 x 3 =16

x = 16-6 = 10

Hence, the fixed charge = ₹ 10

and the charge for each extra day = ₹ 3

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A shopkeeper gives books on...

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Asked on December 30, 2019 by

Ansari Prathyu

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

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ANSWER

Let the fixed charge be x and additional charge be y per day both in Rs.

For Latika, number of days =6=2+4

Therefore, charge x+4y=22

⇒x=22−4y ....(1)

For Anand, number of days =4=2+2

Therefore, charge =x+2y=16

⇒x=16−2y ....(2)

Comparing (1) and (2), we have

22−4y=16−2y

⇒y=3

Substituting this value of y in equation (1), we have

x=22−4×3=10

So, fixed charge = Rs. 10

and additional charge = Rs. 3 per day.

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