Question

A box contains coins of 50 paise, 1 rupee and 2 rupees. For 240 coins in the box, the ratio of 50 paise to 1 rupee to 2 rupees is \[8 & : & 17:15\]. How many 1-rupee coins are there in the box?
A. 48
B. 90
C. 102
D. 108

Answer 1

Hint:- Take the number of coins of the amount as variables. Then equate them to the given ration to find the contribution of each type of coin in the total number of coins in the box. So, use this concept to reach the solution of the given problem.


Complete step-by-step solution -
The total number of coins in the box is 240.
Let the number of 50 paise coins = \[a\]
       the number of 1-rupee coins = \[b\]
       the number of 2 rupees coins = \[c\]
Since the ratio of 50 paise to 1 rupee to 2 rupees is \[8 :17:15\], we have
\[ \Rightarrow a:b:c = 8:17:15\]
We know that in the ratio \[x:y:z = p:q:r\], the \[x`{\text{s}}\] part is given by \[x = \dfrac{p}{{p + q + r}}\], \[y`{\text{s}}\] part is given by \[y = \dfrac{q}{{p + q + r}}\] and \[z`{\text{s}}\] part is given by \[z = \dfrac{r}{{p + q + r}}\].
By using the above formula, consider \[b`{\text{s}}\]part
Therefore, \[b`{\text{s}}\]part is equal to \[\dfrac{{17}}{{8 + 17 + 15}} = \dfrac{{17}}{{40}}\]
Hence the actual number of \[b\]is given by \[\dfrac{{17}}{{40}} \times 240 = 102\] since the total number of coins is 240.
Therefore, the number of 1-rupee coins is 102.
Thus, the correct option is C.

Note: Don`t forget to multiply the obtained 1-rupee coins contributed ratio with the total number of coins to get the number of coins of 1 rupee. In the ratio \[x:y:z = p:q:r\], the \[x`{\text{s}}\] part is given by \[x = \dfrac{p}{{p + q + r}}\], \[y`{\text{s}}\] part is given by \[y = \dfrac{q}{{p + q + r}}\] and \[z`{\text{s}}\] part is given by \[z = \dfrac{r}{{p + q + r}}\].