Sharad bought a table and a fan together for Rs. 5000. After some time he sold the table at the gain of 25 % and the fan at again or 20 %. Thus he gained 23% on the whole. Find the cost of the fan.
Answers
The cost at which Sharad bought the fan is Rs. 2000 .
• Given,
The total cost price of table and fan together = Rs. 5000
• Let the cost price (C.P) of table be x, and the cost price (C.P.) of fan be (5000 - x)
• Profit percent earned on table = 25%
Therefore, selling price (S.P.) of table = {(100 + gain %) / 100} × C.P.
=> S.P. = {(100 + 25) / 100} × x
=> S.P. = (125 / 100) × x
=> S.P. = 125x / 100
• Profit percent earned on fan = 20%
Therefore, selling price (S.P.) of fan = {(100 + gain %) / 100} × C.P.
=> S.P. = {(100 + 20) / 100} × (5000 - x)
=> S.P. = (120 / 100) × (5000 - x)
=> S.P. = {120 (5000 - x)} / 100
• Given,
Overall gain on both table and fan = 23%
Therefore, total selling price (S.P.) of both table and fan = {(100 + overall gain %) / 100} × total C.P.
=> S.P. = {(100 + 23) / 100} × 5000
=> S.P. = (123 / 100) × 5000
=> S.P. = (123 × 5000) / 100
• According to the question,
S.P. of table + S.P. of fan = Total S.P.
=> (125x / 100) + {120 (5000 - x)} / 100) = (123 × 5000) / 100
=> 125x + 120 (5000 - x) = 123 × 5000
=> 125x + (120 × 5000) - 120x = 123 × 5000
=> 125x - 120x = (123 × 5000) - (120 × 5000)
=> 5x = 5000 (123 - 120)
=> 5x = 5000 × 3
=> 5x = 15000
=> x = 15000 / 5
=> x = 3000
• Therefore, the C.P. of the table = Rs. 3000
C.P. of the fan = Rs. (5000 - 3000) = Rs. 2000
• The fan was bought at Rs. 2000 .
the cost of fan which bought by the sharad is Rs.2000