Question

If the cost of a dozen soaps is Rs. 285.60. What will be the cost of 15 such soaps?

A) Rs 827
B) Rs 772
C) Rs 676
D) Rs 357

Answer 1

Hint: 1 dozen soaps = 12 soaps
Here, we are given the cost of 12 soaps as Rs. 285.60. We will calculate the cost of 1 soap & then from the unitary method, we will calculate the cost of 15 soaps.

Complete step by step solution: It is given that cost of a dozen soaps is Rs. 285.60
We know 1 dozen = 12 units
i.e cost of 12 soaps = Rs 285.60

Now we will find the cost of 1 soap

\[\therefore {\text{Cost of 1 soap}} = \dfrac{{{\text{Cost of 12 soaps}}}}{{{\text{ No of Soaps}}}}\]
          $\begin{gathered}
   = \dfrac{{{\text{Rs}}\;285.60}}{{12}} \\
   = {\text{Rs}}\;23.8 \\
\end{gathered} $
∴ Cost of 1 soap = Rs 23.8

Now we got the cost of 1 soap as Rs 23.8. Now, we one asked to calculate the cost of 15 such soaps. Let ‘x’ be the price of 15 soaps. We will use the unitary method now:

1 soap cost → Rs 23.8

15 soap will cost → Rs x.

By unitary method:

$1 \times x = 15 \times {\text{Rs}}\;23.8$
$\therefore x = {\text{Rs}}\;357$

∴ Cost of 15 such soaps = Rs 357

∴ Correct option (D).

Note: We can do this problem directly without calculating the cost of 1 soap. Here is the procedure.
Let the cost of 15 soaps be x

12 soaps cost → Rs 285.60
15 soaps will cost → Rs x.

By unitary method:

$12 \times x = 15 \times {\text{Rs}}\;285.60$
$\therefore x = {\text{Rs}}\dfrac{{285.60 \times 15}}{{12}}$
$\therefore \boxed{x = {\text{Rs}}\;357}$
∴ Cost of 15 soaps = Rs 357.