Raheem sells a machine for Rs 48 lakhs at a loss. Had he sold it for Rs 60 lakh, his gain would have been 5 times the former loss. Find the cost price of the machine.
- ARs 58 lakhs
- BRs 69.6 lakhs
- CRs 42 lakhs
- DRs 50 lakhs
Solution & Step-by-step Explanation
Let the cost price of the machine be CP (in lakhs).
In the first case, the selling price is SP
1
=48 lakhs, which results in a loss:
Loss=CP−48
In the second case, the selling price is SP
2
=60 lakhs, which results in a profit:
Gain=60−CP
According to the question, the gain is 5 times the former loss:
Gain=5×Loss
60−CP=5(CP−48)
60−CP=5CP−240
60+240=5CP+CP
300=6CP
CP=
6
300
=50
Thus, the cost price of the machine is Rs 50 lakhs.
In the first case, the selling price is SP
1
=48 lakhs, which results in a loss:
Loss=CP−48
In the second case, the selling price is SP
2
=60 lakhs, which results in a profit:
Gain=60−CP
According to the question, the gain is 5 times the former loss:
Gain=5×Loss
60−CP=5(CP−48)
60−CP=5CP−240
60+240=5CP+CP
300=6CP
CP=
6
300
=50
Thus, the cost price of the machine is Rs 50 lakhs.