Ex 3.3 Q2 (v) - A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid ₹27 for a book kept for seven days, while Susy paid ₹21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.
Solution:-Let,
Fixed charge for first 3 days = ₹x
Additional charge after 3 days = ₹y per day
➙ It is given that, Saritha paid ₹27 for a book she kept for seven days,
∴ x + (7 - 3)y = 27
∴ x + 4y = 27
∴ x = 27 - 4y ------- (1)
➙ Also Susy paid ₹21 for the book she kept for five days,
∴ x + (5 - 3)y = 21
∴ x + 2y = 21
∴ 27 - 4y + 2y = 21 ------- { from (1) }
∴ 27 - 2y = 21
∴ 2y = 27 - 21
∴ 2y = 6
∴ y =
6
/
2
∴ y = 3
➙ Putting y = 3 in Eqⁿ(1)
∴ x = 27 - 4(3)
∴ x = 27 - 12
∴ x = 15
Therefore,
*Fixed charge for first 3 days
= x
= ₹15
*Additional charge after 3 days
= ₹y per day
= ₹3 per day
Hence,
The fixed charge and the charge for each extra day is ₹15 and ₹3 per day respectively.
------------------------------------
Try This..
✒ A taxi company charges a fixed fare for the first 3 km and a per km charge thereafter. If a person travels 10 km and pays ₹80 while another travels 6 km and pays ₹56, find the charges.
✒ A parking lot charges a fixed amount for the first two hours and a different rate for each additional hour. If Raj paid ₹50 for 5 hours and Ravi paid ₹35 for 3 hours, find the rates.
❌ Common Mistakes
Not defining variables properly:▸ Always clearly define your variables before forming equations. This avoids confusion later.Setting up incorrect equations:▸ Check carefully how the charges are applied before forming the equations.Arithmetic errors while solving:▸ Simple addition/subtraction mistakes can lead to wrong answers. Double-check your calculations.Not verifying the final answer:▸ After finding values for x and y, plug them back into the original equations to ensure they satisfy both equations.
📝 Related Questions:-
- Ex 3.3 Q2 (i) - If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes 1/2 if we only add 1 to the denominator. What is the fraction?
- Ex 3.3 Q2 (ii) - Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?
- Ex 3.3 Q2 (iii) - The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.
- Ex 3.3 Q2 (iv) - Meena went to a bank to withdraw ₹2000. She asked the cashier to give her ₹50 and ₹100 notes only. Meena got 25 notes in all. Find how many notes of ₹50 and ₹100 she received.
Queries Solved:-
Class 10 Ex 3.3
Ex 3.3 Q2 v Class 10
Class 10 Ex 3.3 Q2 v
Class 10 Chap 3 Ex 3.3 Q2 v
Class 10 Pair Of Linear Equations in Two Variables
If you found it helpful, please leave a comment below sharing your thoughts or questions.
Don’t forget to share it with your classmates to help them learn too.
Good luck, and happy learning!
Together, let’s make math simpler and more enjoyable for everyone!