A shopkeeper charges a fixed amount for the first two days and a daily charge thereafter. Latika paid Rs 22 for 6 days; Anand paid Rs 16 for 4 days. Find the fixed charge and the daily charge after two days.
Fixed charge = Rs 10; additional per day = Rs 3.
Step 1: Suppose the fixed charge for the first two days is \(F\).
Step 2: Suppose the extra charge per day (after the first two days) is \(r\).
For Latika:
She stayed for 6 days.
The first 2 days are included in the fixed charge \(F\).
So extra days = \(6 - 2 = 4\).
Extra charge = \(4 \times r = 4r\).
Total money paid by Latika = \(F + 4r = 22\). … (Equation 1)
For Anand:
He stayed for 4 days.
The first 2 days are included in the fixed charge \(F\).
So extra days = \(4 - 2 = 2\).
Extra charge = \(2 \times r = 2r\).
Total money paid by Anand = \(F + 2r = 16\). … (Equation 2)
Now solve the equations:
From Equation (1): \(F + 4r = 22\).
From Equation (2): \(F + 2r = 16\).
Subtract Equation (2) from Equation (1):
(F + 4r) – (F + 2r) = 22 – 16
\(F - F + 4r - 2r = 6\)
\(2r = 6\)
\(r = 3\).
Find F:
Put \(r = 3\) in Equation (2):
\(F + 2(3) = 16\)
\(F + 6 = 16\)
\(F = 10\).
Final Answer:
Fixed charge = Rs 10, and additional daily charge = Rs 3.