Question

A manufacturer sells an item to an angency at a profit of 25%. The agency sells the item to a shopkeeper at 10% profit and the shopkeeper sells the item at the profit of 20%. If the selling price of the item is ₹594. Find the manufacturing price. ​

Answer 1

Let :-

• The manufacturing cost of the items be M

Given :-

• Selling price of an item = ₹594

To Find :-

• The manufacturing cost of item = ?

Solution :-

• To solve this question at first we have to make an equation by helping clue in the question.

Calculation for manufacturer :-

CP for manufacturer :-

• CP = M. P = 25%. SP = ?

⟼ SP = (100 + P%)/100 × CP

⟼ SP = 125/100 × M

⟼ SP = 125M/100

⟼ SP = 5M/4

Calculation for Agency :-

CP for Agency :-

• P = 10% CP = 5M/4. SP = ?

⟼ SP = (100 + P%)/100 × CP

⟼ SP = (110/100) × 5M/4

⟼ SP = 11/10 × 5M/4

⟼ SP = 55M/40

Calculation for Shopkeeper :-

CP for Shopkeeper :-

• CP = 55M/40. P = 20%. SP = ?

⟼ SP = (100 + P%)/100 × CP

⟼ SP = 120/100 × 55M/40

⟼ SP = (3 × 11M)/20

⟼ SP = 33M/20

Calculation for manufacturing cost :-

• SP for Shopkeeper = 33M/20. SP = 594

⟼ 33M/20 = 594

⟼ 33M = 594 × 20

⟼ M = 18 × 20

⟼ M = ₹ 360

Hence, the manufacturing cost = ₹ 360 :-

Answer 2

G I V E N :

A manufacturer sells an item to an angency at a profit of 25%. The agency sells the item to a shopkeeper at 10% profit and the shopkeeper sells the item at the profit of 20%. If the selling price of the item is ₹594. Find the manufacturing price.

S O L U T I O N :

Let us assume the CP be x

CP of the customer = ₹594

SP of the shopkeeper = ₹594

Profit gained = 20%

Now, using

SP = CP + P% of CP

Putting the values we get

$\frak{ \rightharpoondown 594 = x + 20\% \: of \: x } \\ \\ \\ \rightharpoondown \frak{594 = x + \frac{20}{100} \times x} \\ \\ \\ \rightharpoondown\frak{594 = (\frac{100 + 20}{100})x} \\ \\ \\ \rightharpoondown \frak{594 = \frac{120}{100}x } \\ \\ \\ \rightharpoondown \frak{x = 594 \times \frac{100}{120} } \\ \\ \\ \star \: \: \underline{ \boxed{ \red{\frak{495}}}}$

AGENCY

Using the same as the previous one

SP = CP + P% of CP

SP = ₹495

P% = 10%

Now, let us assume the CP for the agency be y

$\frak{ \rightharpoondown 495= y+ 10\% \: of \: y } \\ \\ \\ \rightharpoondown \frak{495 = y + \frac{10}{100} \times y} \\ \\ \\ \rightharpoondown\frak{495 = (\frac{100 + 10}{100})y} \\ \\ \\ \rightharpoondown \frak{495 = \frac{110}{100}y } \\ \\ \\ \rightharpoondown \frak{y = 495 \times \frac{100}{110} } \\ \\ \\ \star \: \: \underline{ \boxed{ \red{\frak{450}}}}$

MANUFACTURER

SP = CP + P% of CP

Let us assume the CP for the manufacturer be z

SP = ₹450

P% = 25%

$\frak{\rightharpoondown 450 = z + 25\% \: of \: z} \\ \\ \\ \rightharpoondown \frak{450 = z+ \frac{25}{100} \times z} \\ \\ \\ \rightharpoondown\frak{450 = (\frac{100 + 25}{100})z} \\ \\ \\ \rightharpoondown \frak{450 = \frac{125}{100}z } \\ \\ \\ \rightharpoondown \frak{z = 450 \times \frac{100}{125} } \\ \\ \\ \star \: \: \underline{ \boxed{ \red{\frak{360}}}}$

• The manufacturer's price is ₹360