question_answer 17)

                The organisers of an essay competition decide that a winner in the competition gets a prize of Rs. 100 and a participant who does not win gets a prize of Rs. 25. The total prize money distributed is Rs. 3,000. Find the number of winners, if the total number of participants is 63.

Answer:

                Let the number of winners be \[x\]. \[\because \]     The total number of participants is 63. \[\therefore \] The number of non-winners \[=63-x\] Prize money got by winners \[=\text{Rs}\text{.}\,\,x\,\times 100=\text{Rs}\text{.}\,\,100x\] Prize money got by non-winners \[=\text{Rs}\text{.}\,(63-x)\times 25\] \[=\text{Rs}\text{.}\,(1575-25x)\] \[\because \]     The total prize money distributed is Rs. 3000. \[\therefore \]  \[100x+(1575-25x)\,=3000\] \[\Rightarrow \]               \[75x+1575=3000\] \[\Rightarrow \]               \[75x=3000-1575\]           |Transposing 1575 to RHS \[\Rightarrow \]               \[75x=1425\] \[\Rightarrow \]               \[x=\frac{1425}{75}=19\]                              | Dividing both sides by 75 Hence, the number of winners is 19. Check: \[19+(63-19)=63\] \[19\times 100+(63-19)\times 25\] \[=1900+44\times 25\]  |as desired \[=1900+1100=3000\]