Question

The profit made by a certain dealer is equal to T% of SP and P% of CP. Show that P=100T/100-T.

Answer 1

Answer:

See explanation

Step-by-step explanation:

CP = cost price

SP = selling price

Profit = SP - CP

Given:

Profit = T% of SP

=> Profit = (T/100)*SP .........(i)

Profit = P% of CP

=> Profit = (P/100)*CP .....(ii)

Equating (i) and (ii), we get:

$\frac{T}{100} * SP = \frac{P}{100} * CP$

T*SP = P*CP

=> P = T * (SP/CP) ........(iii)

Now,

Profit = P% of CP .........from (i)

=> SP - CP = (P/100)*CP

Divide throughout by CP

=> (SP/CP) - 1 = (P/100)

=> (SP/CP) = (P/100) + 1 ........(iv)

Subtitute (SP/CP) as obtained in (iv) in (iii)

=> P = T*[(P/100) + 1}

=> P = (PT/100) + T

=> P - (PT/100) = T

=> P*(1 -(T/100)) = T

=> P*[(100 - T)/100] = T

=> P*(100 - T) = 100*T

=> P = (100*T) / (100 - T)

The last few steps have been done in equation mode for better understanding.

$P = T(\frac{P}{100} + 1)$

$P = \frac{PT}{100} + T$

$P - \frac{PT}{100} = T$

$P(1 - \frac{T}{100} ) = T$

$P(\frac{100-T}{100} ) = T$

$P = \frac{100T}{100-T}$