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Hint: The unitary method, in essence, is all about finding the “per unit value”. The unitary method is a technique for solving a problem by first finding the value of a single unit.

Complete step-by-step answer:

Now use the unitary method to find the value of a single unit.

Cost of a dozen pens (12 pens) \[ = Rs.180\]

Cost of one pen $ = \dfrac{{180}}{{12}}$

Cost of one pen, ${C_1} = Rs.15$

Now, Cost of 8 ball pens $ = Rs.56$

Cost of one ball pen $ = \dfrac{{56}}{8}$

Cost of one ball pen, ${C_2} = Rs.7$

Now, take the ratio of cost of a pen to the cost of a ball pen.

$\dfrac{{{C_1}}}{{{C_2}}} = \dfrac{{15}}{7}$

So, the ratio of the cost of a pen to the cost of a ball pen is 15:7

Note:Whenever we face such types of problems we use some important points. First we find the value of a single unit by using a unitary method then after the take ratio we can get the required answer.

Complete step-by-step answer:

Now use the unitary method to find the value of a single unit.

Cost of a dozen pens (12 pens) \[ = Rs.180\]

Cost of one pen $ = \dfrac{{180}}{{12}}$

Cost of one pen, ${C_1} = Rs.15$

Now, Cost of 8 ball pens $ = Rs.56$

Cost of one ball pen $ = \dfrac{{56}}{8}$

Cost of one ball pen, ${C_2} = Rs.7$

Now, take the ratio of cost of a pen to the cost of a ball pen.

$\dfrac{{{C_1}}}{{{C_2}}} = \dfrac{{15}}{7}$

So, the ratio of the cost of a pen to the cost of a ball pen is 15:7

Note:Whenever we face such types of problems we use some important points. First we find the value of a single unit by using a unitary method then after the take ratio we can get the required answer.