Raghunandan sells a machine for ₹45 lakhs at a loss. Had he sold it for ₹55 lakh, his gain would have been 9 times the former loss. Find the cost price of the machine.
- ARs 54 lakhs
- BRs 46 lakhs
- CRs 60 lakhs
- DRs 38 lakhs
Solution & Step-by-step Explanation
Let the Cost Price (CP) of the machine be x lakhs.
In the first case, selling price (SP
1
) = ₹45 lakhs (Loss case):
Loss=CP−SP
1
=x−45
In the second case, selling price (SP
2
) = ₹55 lakhs (Gain case):
Gain=SP
2
−CP=55−x
According to the given condition, the gain is 9 times the loss:
Gain=9×Loss
55−x=9(x−45)
55−x=9x−405
55+405=9x+x
460=10x
x=46
So, the cost price of the machine is ₹46 lakhs.
In the first case, selling price (SP
1
) = ₹45 lakhs (Loss case):
Loss=CP−SP
1
=x−45
In the second case, selling price (SP
2
) = ₹55 lakhs (Gain case):
Gain=SP
2
−CP=55−x
According to the given condition, the gain is 9 times the loss:
Gain=9×Loss
55−x=9(x−45)
55−x=9x−405
55+405=9x+x
460=10x
x=46
So, the cost price of the machine is ₹46 lakhs.