Question

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

• A. The number of Rs 5 coins are 30,
  number of Rs 2 coins are 70 and,
  the number of Re 1 coins are 60
• B. The number of Rs 5 coins are 10,
  number of Rs 2 coins are 50 and,
  the number of Re 1 coins are 100
• C. The number of Rs 5 coins are 20,
  number of Rs 2 coins are 60 and,
  the number of Re 1 coins are 80
• D. The number of Rs 5 coins are 15,
  number of Rs 2 coins are 75 and,
  the number of Re 1 coins are 70

Answer 1

Answer: (C)

The number of Rs 5 coins are 20,

number of Rs 2 coins are 60 and,
the number of Re 1 coins are 80
Let the number of Rs $5$ coins be $x$.
Then, number of Rs $2$ coins $=3x$ and
the number of Re $1$ coins $=160-x-3x=160-4x$ .... (Since, total number of coins are $160$)
Now, value of Rs $5$ coins $=Rs(5\times x)=Rs5x$ and
Value of Rs $2$ coins $=Rs(2\times 3x)=Rs6x$
Given, total value of money $=Rs300$
$\therefore 5x+6x+(160-4x)=300$

$\Rightarrow 7x+160=300$

$\Rightarrow 7x=300-160$ .... [Transposing $160$ to RHS]

$\Rightarrow 7x=140$

$\Rightarrow x=20$ ...... [Dividing both sides by $7$]
Thus, the number of Rs $5$ coins $=20$,
Number of Rs $2$ coins $=60$ and the number of Re $1$ coins $=80$