Question

I have a total of Rs. 300 in coins of denominator Rs 1, Rs 2, Rs 5. The number of Rs 2 coins is 3 times the no. of Rs 5 coins. The total number of coins is 160. How many coins of each combination are with me?

Answer 1

Hint: In this, first we can find number of coins of each in terms on one variable then we can make equation in terms of its total value equal to Rs. 300

Complete step-by-step solution -
As given, the total number of coins is 160.
Let the number of Rs. 5 coins = x
Then number of Rs. 2 coins = 3x
Hence we can write
$\Rightarrow Number\,of\,Rs.1\,coins\,+Number\,of\,Rs.2\,coins\,+Number\,of\,Rs.5\,coins\,=160$
$\Rightarrow Number\,of\,Rs.1\,coins\,+3x+x\,=160$
$\Rightarrow Number\,of\,Rs.1\,coins\,=160\,-\,4x$
Therefore,
Total Rs = (Rs 1 \[\times \]Number of Rs 1 coin) \[+\] (Rs 2 \[\times \] Number of 2 coins) \[+\](Rs5 \[\times \]Number of Rs 5 coins)
\[\Rightarrow 300=[1\times (160-4x)]+(2\times 3x)+(5\times x)\]
\[\Rightarrow 300=160-4x+6x+5x=160-4x+11x\]
\[\Rightarrow 300=160+7x\]
$\Rightarrow 7x=300-160$
$\Rightarrow 7x=140$
$\Rightarrow x=\dfrac{140}{7}=20$
Hence, number of coins of Rs 5 = 20
As we let number of Rs.2 coins = 3x
On substituting x = 20
Number of Rs.2 coins = 60
As we have number of Rs.1 coins =
On substituting x = 20
$\Rightarrow 160-4\times 20$
$\Rightarrow 80$
Number of Rs.1 coins = 80.

Note: In this question when we will solve the equation we will get only the number of Rs. 5 coins. So we need to put value in that expression which we let for a number of Rs. 2 coins and Rs.1 coins. Otherwise we will not get a complete answer.