Question

A lady has Rs 2 and Rs 1 coins in her purse. If in all she has 60 coins, totaling Rs 105, how many of each type of coins does she have?
A. 50, 15
B. 45, 20
C. 45, 15
D. None

Answer 1

Hint: Here, we assume number of coins of Rs 2 be x, then total amount of Rs 2 coins is Rs 2x; and number of coins of Rs 1 be y, then total amount of Rs 1 coins is Rs y and change the given statements are linear equations, then solve the linear equations to get the number of coins.

Complete step by step answer:
Given, the lady has only Rs 2 and Rs 1 coins in her purse and the total number of coins is 60.
Let the number of coins of Rs 2 be x and the number of coins of Rs 1 be y.
Then, \[x + y = 60\] …(i)
Also given the total amount in her purse is Rs 105.
Then, $2x + y = 105$ …(ii)
Now, we observe that equation (i) and equation (ii) are linear equations in two variables with variables x and y, by solving these two equations we get values of x and y.
Solving equations (i) and (ii) by elimination method.
Subtracting equation (i) from equation (ii)
$\left( {2x + y} \right) - \left( {x + y} \right) = 105 - 60$
$2x + y - x - y = 45$
$x = 45$
Putting the value of x in equation (i), we get
$45 + y = 60$
$y = 60 - 45$
$y = 15$
Here, $x + y = 45 + 15 = 60$ and $2x + y = 2 \times 45 + 15 = 90 + 15 = 105$ both x and y satisfy equation (i) and equation (ii).
Therefore, the number of coins of Rs 2 is 45 and the number of coins of Rs 1 is 15.

Hence, option (C) is correct.

Note:
In money related problems always be careful while changing the statements into equations because in coins or note related problems, the total amount of a particular coin depends on the number of coins and value of that coin. You can solve the linear equations by any of the following algebraic methods, Substitution method, Cross-multiplication method and elimination method.