Question

I have a total of rupees 300 in coins of denominations rupee 1, rupee 2, and rupee 5. The number of rupee 2 coins is 3 times the number of rupee 5 coins. The total number of coins is 160. How many coins of each denomination are with me?

Answer 1

let the no. of rs 5 coins be $x$

& the no. of rs 1 coin be $y$

& no. of rs 2 coins be $3x$

According to the question, total no. of coins $=160$

$x+3x+y=160$

$4x+y=160$ ..........eq. 1

again according to the question total rs $=300$

$5x+2\left(3x\right)+1y=300$

$11x+y=300$......... eq. 2

by elimination method

on subtracting both the equations

$4x+y-11x-y=160-300$

$\Rightarrow -7x=-140$

$\Rightarrow x=20$

on putting the the value of $x$ in eq 2

$4\left(20\right)+y=160$

$80+y=160$

$y=80$

Hence,

no of rs 2 coins $=3\left(20\right)=60$

no. of rs 5 coins $=20$

no. of rs 1 coins$=80$