A shopkeeper sold an article for Rs. 540 at some profit. Had he sold it for Rs. 470, then there would have been a loss equal to one-sixth of the initial profit. What was the cost price (in Rs.) of the article?
- A525
- B480
- C505
- D540
Solution & Step-by-step Explanation
Let the Cost Price of the article be Rs. CP, and the initial profit be P.
From the first condition:
Selling Price
1
=CP+P⟹540=CP+P— (Equation 1)
From the second condition, the loss is equal to
6
1
P:
Selling Price
2
=CP−Loss⟹470=CP−
6
1
P— (Equation 2)
Subtract Equation 2 from Equation 1:
540−470=P−(−
6
1
P)
70=P+
6
1
P
70=
6
7
P⟹P=60
Substitute P=60 into Equation 1:
540=CP+60⟹CP=540−60=480
From the first condition:
Selling Price
1
=CP+P⟹540=CP+P— (Equation 1)
From the second condition, the loss is equal to
6
1
P:
Selling Price
2
=CP−Loss⟹470=CP−
6
1
P— (Equation 2)
Subtract Equation 2 from Equation 1:
540−470=P−(−
6
1
P)
70=P+
6
1
P
70=
6
7
P⟹P=60
Substitute P=60 into Equation 1:
540=CP+60⟹CP=540−60=480