Question

There are 34000 rupees in a bag in the denomination of Rs 50, Rs 100, Rs 500 and Rs 1000 currency notes. If the ratio of the number of these notes is 2: 3: 4 : 1 then find the number of notes of 500 denomination.
(a) 20
(b) 40
(c) 30
(d) 50

Answer 1

Hint: Here, as the ratio of the number of the denominations of each type is given to be 2: 3: 4: 1. So, we will consider the denominations of each type as 2x, 3x, 4x and x. Using the number of each type of the denominations, we will find their total values in rupees. Thereafter, we will equate the sum of all these values to 34,000 to get the value of x and once we get the value of x, we can easily find the number of denominations of each type.

Complete step-by-step answer:
Since, the ratio of the number of notes of Rs 50, Rs 100, Rs 500 and Rs 1000 is 2: 3: 4: 1. So, let us consider that:
Number of notes of denomination Rs 50 = 2x
Number of notes of denomination Rs 100 = 3x
Number of notes of denomination Rs 500 = 4x
Number of notes of denomination Rs 1000 = x
Since, we know that the total money contained in the bag is Rs 34,000. This means that the amount that each of these denominations signify must sum up to Rs 34,000.
So, total amount when 2x notes of denomination Rs 50 is taken = $2x\times 50$.
Similarly, for denominations of Rs 100, Rs 500 and Rs 1000, the amount is $3x\times 100,\text{ }4x\times 500\text{ and }x\times 1000$ respectively.
Therefore, we can write:
\[\begin{align}
  & 2x\times 50+3x\times 100+4x\times 500+x\times 1000=34000 \\
 & \Rightarrow 100x+300x+2000x+1000x=34000 \\
 & \Rightarrow 3400x=34000 \\
 & \Rightarrow x=\dfrac{34000}{3400}=10 \\
\end{align}\]
So, the value of x comes out to be 10.
Therefore, number of notes of denominations Rs 500 = $4x=4\times 10=40$
Hence, option (b) is the correct answer.

Note: Here, a chance of mistake is that the students may take the incorrect ratio for a denomination. The ratio always has to be taken in the same order in which the denominations are given in the problem, that is, each denomination has to be multiplied with its corresponding ratio. The calculations must be done properly.