A salesman sold an article at three-fifth of the marked price. By doing so, he gained 20%. The ratio of the marked price and the cost price of the article is:
- A4 ∶ 1
- B1 ∶ 3
- C1 ∶ 2
- D2 ∶ 1
Solution & Step-by-step Explanation
Let the marked price (MP) of the article be M and the cost price (CP) be C.
According to the question, the selling price (SP) is three-fifth of the marked price:
SP=
5
3
M
By selling at this price, the salesman gains 20%. Therefore:
SP=CP×(1+
100
20
)=
100
120
C=
5
6
C
Equating both expressions for SP:
5
3
M=
5
6
C
Multiplying both sides by 5:
3M=6C
C
M
=
3
6
=
1
2
Thus, the ratio of the marked price and the cost price is 2:1.
According to the question, the selling price (SP) is three-fifth of the marked price:
SP=
5
3
M
By selling at this price, the salesman gains 20%. Therefore:
SP=CP×(1+
100
20
)=
100
120
C=
5
6
C
Equating both expressions for SP:
5
3
M=
5
6
C
Multiplying both sides by 5:
3M=6C
C
M
=
3
6
=
1
2
Thus, the ratio of the marked price and the cost price is 2:1.