Partnership and Discount

Question: A, B and C together invest Tk. 53000 in a business. A invests Tk. 5000 more than B and B invests Tk. 6000 more than C. Out of a total profit of Tk. 31800, find the share of A.

Solution:
Let C's investment = x
 Then,
B invests Tk. 6,000 more than C
∴ B = x + 6000
A invests Tk. 5000 more than B
∴ A = (x + 6000) + 5000 = x + 11000

Total investment,
A + B + C = 53000
⇒ (x + 11000) + (x + 6000) + x = 53000
⇒ 3x + 17000 = 53000
⇒ 3x = 36000  
∴  x = 12000 

Now,
C = x = 12000
B = 12000 + 6000 = 18000
A = 12000 + 11000 = 23000

∴ Profit sharing ratio is,
A : B : C = 23000 : 18000 : 12000 = 23 : 18 : 12

∴ Share of A = 31800 × (23/53) = Tk. 13800

Question: A man bought a book for Tk. 360 after getting a 20% discount. What was the original catalog price of the book?

Solution:
20% discount,
If the catalog price is Tk. 100 then the purchased price = (100 - 20) = Tk. 80

Now,
If the purchase price is Tk. 80, the catalog price = 100 taka.
If the purchase price is Tk. 1, the catalog price = 100/80 taka
If the purchase price is Tk. 360, the catalog price = (100 × 360)/80
= Tk. 450

Question: Having incurred a 20% loss on a saree sold for TK 3200, a shopkeeper now wishes to set a marked price that allows for a 25% profit, even after applying an 10% discount. What is that price?

Solution:
After selling a saree for TK. 3200 a shopkeeper suffers a loss of 20%.

Selling price TK. 80 when cost price TK. 100
∴ selling price TK. 3200 when cost price = TK. (100 × 3200)/80
= TK. 4000

25% profit,
cost price TK. 100 then selling price TK. 125
∴ cost price TK. 4000 then selling price = TK. (125 × 4000)/100
= TK. 5000

discount 10%
selling price TK. 90 when marked price = TK. 100
∴ selling price TK. 5000 when marked price = (100 × 5000)/90
= TK. 5555.55 

Let the total investment be Tk. z
Then, 20% of z = 98000
⇒ z = 98000 × 100)/20
= 490000.
Let the capitals of P, Q and R be Tk. 5x, Tk. 6x and Tk. 6x respectively.
Then, (5x × 12) + (6x 12) + (6x × 6) = 490000 × 12
⇔ 168x = 490000 × 12 ⇔ x = (490000 × 12)/168 = 35000.
∴ R's investment = 6x = Tk. (6 × 35000)
= Tk. 210000.

(B.D.×T.D)/(B.D.−T.D)
= Tk (72×60/ 72−60)
= Tk. (72×60/12)
= Tk.360

Let Mr. Y's capital be Tk. P
Mr.X's investment = Tk. 7000 for 24 months
Mr.Y's investment = Tk. P for 14 months
we know that, Profit ratio = investing ratio
According to the question,
(7000 x 24) : (P x 14) = 2 : 3
⇒ 168000 : 14P = 2 : 3
⇒ 12000 : P = 2 : 3
⇒ 12000/P = 2/3
⇒ P = (3 x 12000)/2
⇒ P = 18000.
The required answer is Tk. 18,000.

Banker's Discount for 3/2 years = Tk. 558
Banker's Discount for 2 years = Tk. {558 × (2/3) × 2}
= Tk. 744
True Discount for 2 years = Tk. 600
∴ Sum = {(B.D × T.D)/(B.D - T.D)}
= Tk. {(744 × 600)/(744 - 600)
= Tk. (744 × 600)/144
= TK. 3100
Thus, Tk. 744 is Simple Interest on Tk. 3100 for 2 years
∴ Rate = {(100 × 744)/(3100 × 2)}%
= 12%

Let the marked price of the item be Tk. 100x
Discount % = 20%
Changes for delivery and packaging
= 10% on discounted price

Then
20% discount of 100x = 80x
Charges 10% on the discount price 80x = 88x
⇒ 88x + 88x × (25/100) - 88x = 2046
⇒ 110x - 88x = 2046
⇒ 22x = 2046
⇒ x = 93
Hence, 100x = 93 × 100
= 9300
Marked price = Tk. 9300

A, B and C are partners of a company. During a particular year A received one-fifth of the profit, B received one-third of the profit and C received the remaining Tk 5600. How much did B receive?

Solution:
Let the total profit be Tk x.

Now, Total profit - A's share - B's Share = C's share
⇒ x - (x/5 + x/3) = 5600
⇒ x - {(3x + 5x)/15} = 5600
⇒ x - (8x/15) = 5600
⇒ (15x - 8x)/15 = 5600
⇒ 7x/15 = 5600
⇒ 7x = 5600 × 15
⇒ 7x = 84000
⇒ x = 84000/7
∴ x = 12000

So, B's share = 12000 × 1/3 = 4000