A pharmacist found received 7/5times as many prescriptions for pain killers

 A pharmacist found received 7/5times as many prescriptions for pain killers as he did for traquizers,if a certain dayhe received 72 prescription , then find the no. of prescription for both types 

Let's denote the number of prescriptions for tranquilizers as $T$. According to the problem, the number of prescriptions for pain killers is $\frac{7}{5}$ T times the number of prescriptions for tranquilizers. Therefore, the number of prescriptions for pain killers is $\frac{7}{5}\mathrm{T.}$

We know that the total number of prescriptions received is 72. Therefore, we can set up the following equation:

$$T + \frac{7}{5}T = 72$$

Combine the terms on the left side:

$$\frac{5}{5}T + \frac{7}{5}T = \frac{12}{5}T$$

Thus, the equation becomes:

$$\frac{12}{5}T = 72$$

To solve for $T$, first multiply both sides of the equation by 5 to clear the fraction:

$$12T = 72 \times 5$$

                                                                Calculate $72\times \mathrm{<span\; class="base"><span\; class="strut"></span><span\; class="mord">5</span></span><br>}$

$$72 \times 5 = 360$$

                                                                      So:

$$12T = 360$$

                 Now, divide both sides by 12 to solve for $T$:

$$T = \frac{360}{12}$$ $$T = 30$$

So, the number of prescriptions for tranquilizers is 30.

To find the number of prescriptions for pain killers:

$$\text{Number of pain killer prescriptions} = \frac{7}{5} \times T = \frac{7}{5} \times 30$$

Calculate:

$$\frac{7}{5} \times 30 = 7 \times 6 = 42$$

Thus, the number of prescriptions received for pain killers is $\boxed{42}$.