A discount series of p% and q% on an invoice is the same as a single discount of -
A. $$\left[ {p + q + \frac{{pq}}{{100}}} \right]\% $$
B. $$\left[ {p - q + \frac{{pq}}{{100}}} \right]\% $$
C. $${\text{100 - }}\left[ {p + q + \frac{{pq}}{{100}}} \right]\% $$
D. None of these
Answer: Option D
Solution(By Examveda Team)
Let marked price be Rs. 100Then,
S.P. = (100 - q)% of (100 - p)% of Rs. 100
$$\eqalign{ & = {\text{Rs}}{\text{.}}\left[ {\frac{{100 - {\text{q}}}}{{100}} \times \frac{{100 - {\text{p}}}}{{100}} \times 100} \right] \cr & = {\text{Rs}}.\left[ {\frac{{\left( {100 - {\text{q}}} \right)\left( {100 - {\text{p}}} \right)}}{{100}}} \right] \cr & \therefore {\text{Single discount }} \cr & = \left\{ {100 - \left[ {\frac{{\left( {100 - {\text{q}}} \right)\left( {100 - {\text{p}}} \right)}}{{100}}} \right]} \right\}\% \cr & = \left( {{\text{p}} + {\text{q}} - \frac{{{\text{pq}}}}{{100}}} \right)\% \cr} $$
Related Questions on Profit and Loss
A. 45 : 56
B. 45 : 51
C. 47 : 56
D. 47 : 51
A. Rs. 2600
B. Rs. 2700
C. Rs. 2800
D. Rs. 3000
A. A neither losses nor gains
B. A makes a profit of 11%
C. A makes a profit of 20%
D. B loses 20%
A. Rs. 3,750
B. Rs. 3,250
C. Rs. 2,750
D. Rs. 2,250
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