Question

Ram has Rs.27 in the form of fifty paise and twenty five paise coins. He has twice as many twenty five paise coins as he has fifty paise coins. The number of coins of each kind is,
A.\[22\;and\;50\]
B.\[27\;and\;54\]
C,\[20\;and\;50\]
D.\[30\;and\;40\]
E.None of these

Answer 1

Hint: Here we have to add the amount of fifty paise and twenty five paise to get the overall amount of Rs.27. We know that four coins of twenty five paise makes a rupee and two coins of fifty paise makes a rupee. So we will consider x coins of fifty paise and 2x coins of twenty five paise. Then we will multiply the denominations by its value compared with a rupee and equate it to Rs.27. this equation when solved will give the value of x and then the number of coins.

Complete step by step solution:
Let x be the number of fifty paise coins.
Given that Ram has twice as many twenty five paise coins as he has fifty paise coins.
Thus the number of coins of twenty five paise will be 2x.
Now the amount of these coins will be,
\[\dfrac{1}{2}x + \dfrac{1}{4}\left( {2x} \right) = 27\]
On solving the ratios we get,
\[\dfrac{1}{2}x + \dfrac{1}{2}x = 27\]
On adding we get,
\[x = 27\]
This gives the number of coins of fifty paise coins.
Now the number of coins of twenty five paise will be 2x. Thus it will be \[2x = 2 \times 27 = 54\]
Thus we get the answer as \[27\& 54\] .
So option B is correct.
So, the correct answer is “Option B”.

Note: Here note that value of x is 27 but total amount also equals to 27, but value of x is the number of coins. Here coincidentally both are the same. So don’t get confused. Also note that in options only option B is the option having the numbers in the form as second is twice or other. So that is the only answer. But this is observed only in this case. So in general we will go for the method mentioned above.