Question

A bill of Rs. \[40\] is paid by means of Rs. $5$ notes and Rs. $10$ notes. Seven notes are used in all. If x is the number of Rs. $5$ notes and y is the number of Rs. $10$ notes, then
A. \[x + y = 7\] and \[x + 2y = 40\]
B. \[x + y = 7\] and \[x + 2y = 8\]
C. \[x + y = 7\] and \[2x + y = 8\]
D. \[x + y = 7\] and \[2x + y = 40\]

Answer 1

Hint:In the question, it is given that the total amount of bill is Rs. \[40\] and there are only two types of notes i.e., Rs. $5$ having x number of notes and Rs. $10$ having y number of notes, which makes this a linear equation in two variables and can be solved easily by forming equations as required.

Complete step-by-step answer:
According to the question, the total amount of bill is Rs. \[40\] and the total number of notes are seven.
Given that the number of Rs. $5$ notes \[ = x\]
So, the total value of Rs. $5$ notes $ = $ (Amount of one note) $ \times $ (Total number of notes)
Or, the total value of Rs. $5$ notes $ = 5.x$
Given that the number of Rs. $10$ notes $ = y$
So, the total value of Rs. $10$ notes $ = $ (Amount of one note) $ \times $ (Total number of notes)
Or, the total value of Rs. $10$ notes $ = 10.y$
Therefore, the total amount of bill $ = $ total value of Rs. $5$ notes $ + $ total value of Rs. $10$ notes
Or, \[40 = 5x + 10y\]
Or, \[x + 2y = 8\]
And, the total number of notes $ = $ the number of Rs. $5$ notes $ + $ the number of Rs. $10$ notes
Or, \[x + y = 7\]
Therefore, \[x + y = 7\] and \[x + 2y = 8\] is the required answer.

So, the correct answer is “Option B”.

Note:Never forget to notice the units of all the given data. Always convert the units in the same format before starting the solution like rupees to paisa or vice versa. Also keep in mind to convert the equations in simplest form possible.