Question

23. A lending library has a fixed charge for the first three
days and an additional charge for each day thereafter.
Sanchit paid * 45 for a book kept for 7 days, while
Karan paid * 25 for the book he kept for 5 days.
The fixed charge and the charge for each extra day
is
(1) * 5 and 10
(2) * 10 and 5
(3) 15 and 5
(4) * 5 and 15​

Answer 1

Answer: Let the fixed charge for 3 days =x and additional charge =y

Let the fixed charge for 3 days =x and additional charge =yAccording to the question

Let the fixed charge for 3 days =x and additional charge =yAccording to the question⇒x+4y=27....eq1

Let the fixed charge for 3 days =x and additional charge =yAccording to the question⇒x+4y=27....eq1⇒x+2y=21....eq2

Let the fixed charge for 3 days =x and additional charge =yAccording to the question⇒x+4y=27....eq1⇒x+2y=21....eq2Subtract eq1 and eq2

Let the fixed charge for 3 days =x and additional charge =yAccording to the question⇒x+4y=27....eq1⇒x+2y=21....eq2Subtract eq1 and eq2⇒(3x+4y=27)−(3x+2y=21)⇒2y=6⇒y=3

Let the fixed charge for 3 days =x and additional charge =yAccording to the question⇒x+4y=27....eq1⇒x+2y=21....eq2Subtract eq1 and eq2⇒(3x+4y=27)−(3x+2y=21)⇒2y=6⇒y=3put y=3 in eq1

Let the fixed charge for 3 days =x and additional charge =yAccording to the question⇒x+4y=27....eq1⇒x+2y=21....eq2Subtract eq1 and eq2⇒(3x+4y=27)−(3x+2y=21)⇒2y=6⇒y=3put y=3 in eq1⇒x+4×3=27⇒x=15

Let the fixed charge for 3 days =x and additional charge =yAccording to the question⇒x+4y=27....eq1⇒x+2y=21....eq2Subtract eq1 and eq2⇒(3x+4y=27)−(3x+2y=21)⇒2y=6⇒y=3put y=3 in eq1⇒x+4×3=27⇒x=15 Fixed charges = Rs. 15

Let the fixed charge for 3 days =x and additional charge =yAccording to the question⇒x+4y=27....eq1⇒x+2y=21....eq2Subtract eq1 and eq2⇒(3x+4y=27)−(3x+2y=21)⇒2y=6⇒y=3put y=3 in eq1⇒x+4×3=27⇒x=15 Fixed charges = Rs. 15The charge for each extra day = Rs. 3

Let the fixed charge for 3 days =x and additional charge =yAccording to the question⇒x+4y=27....eq1⇒x+2y=21....eq2Subtract eq1 and eq2⇒(3x+4y=27)−(3x+2y=21)⇒2y=6⇒y=3put y=3 in eq1⇒x+4×3=27⇒x=15 Fixed charges = Rs. 15The charge for each extra day = Rs. 3

Answer 2

Answer :-

Option (1) is correct.

Step by step calculation :-

Let assume that

• Fixed charge for 3 days be ₹ x

• Per day additional charge be ₹ y.

According to first condition,

Sanchit paid ₹ 45 for a book kept for 7 days.

It means, Sanchit kept for 4 extra days.

$\rm :\longmapsto\:x + 4y = 45 - - - (1)$

According to second condition,

Karan paid ₹ 25 for a book kept for 5 days.

It means, Karan kept for 2 extra days.

$\rm :\longmapsto\:x + 2y = 25 - - - (2)$

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

$\rm :\longmapsto\:2y = 20$

$\bf\implies \:y = 10$

On substituting the value of y in equation (2), we get

$\rm :\longmapsto\:x + 2 \times 10 = 25$

$\rm :\longmapsto\:x + 20 = 25$

$\bf\implies \:x = 5$

Hence,

• Fixed charge for 3 days be ₹ 5

• Per day additional charge be ₹ 10

Basic Concept Used :-

Writing Systems of Linear Equation from Word Problem.

1. Understand the problem.

• Understand all the words used in stating the problem.

• Understand what you are asked to find.

2. Translate the problem to an equation.

• Assign a variable (or variables) to represent the unknown.

• Clearly state what the variable represents.

3. Carry out the plan and solve the problem.