Rajeev sells a machine for Rs 55 lakhs at a loss. Had he sold it for Rs 67 lakh, his gain would have been 5 times the former loss. Find the cost price of the machine.
- ARs 65 lakhs
- BRs 57 lakhs
- CRs 78 lakhs
- DRs 49 lakhs
Solution & Step-by-step Explanation
Let the cost price of the machine be CP lakhs.
In the first case, he sells it at a loss for Rs 55 lakhs:
Loss=CP−55
In the second case, he sells it for Rs 67 lakhs and makes a profit:
Gain=67−CP
Given that the gain is 5 times the former loss:
67−CP=5(CP−55)
67−CP=5CP−275
67+275=5CP+CP
342=6CP
CP=
6
342
=57 lakhs
Thus, the cost price of the machine is Rs 57 lakhs.
In the first case, he sells it at a loss for Rs 55 lakhs:
Loss=CP−55
In the second case, he sells it for Rs 67 lakhs and makes a profit:
Gain=67−CP
Given that the gain is 5 times the former loss:
67−CP=5(CP−55)
67−CP=5CP−275
67+275=5CP+CP
342=6CP
CP=
6
342
=57 lakhs
Thus, the cost price of the machine is Rs 57 lakhs.