A certain number of the capsule were purchased for Rs. 176. Six more capsule could have been purchased in the same amount if each capsule were cheaper by Rs. 3. What was the number of capsules purchased?

Solution (By Examveda Team)

Let Price of each capsule were Rs. X, originally.
So, Number of capsule purchased originally,
= $$ \frac{{176}}{{\text{X}}}$$
If price of capsule is Rs. 3 less then 6 more capsule were purchased. In this case, the number of capsules,
= $$ \frac{{176}}{{{\text{X}} - 3}}$$

According to question,
$$\eqalign{ & \frac{{176}}{{{\text{X}} - 3}} - \frac{{176}}{{\text{X}}} = 6 \cr & \frac{{176{\text{X}} - 176{\text{X}} + 528}}{{{\text{X}} \times \left( {{\text{X}} - 3} \right)}} = 6 \cr & 6{{\text{X}}^2} - 18{\text{X}} - 528 = 0 \cr & {{\text{X}}^2} - 3{\text{X}} - 88 = 0 \cr & {{\text{X}}^2} - 11{\text{X}} + 8{\text{X}} - 88 = 0 \cr & \left( {{\text{X}} - 11} \right)\left( {{\text{X}} + 8} \right) = 0 \cr} $$
Either,
X = 11
Or, X = -8 (Price cannot be negative)
Thus, X = Rs. 11 Hence,
Number of the capsule purchased = $$\frac{{176}}{{11}}$$ = 16