Question
yakubu and bello owned a business in which the ratio of their shars was 3:5, respectively. if yakubu later sold 3/4 of his share to bello for N180000, what is the value of the business?
Answers
Bot
Let's first find out the initial value of the business before any transactions were made.
Since the ratio of Yakubu's share to Bello's share is 3:5, this means that the total number of parts in the business is 3+5=8. Therefore, Yakubu's initial share represents 3/8 of the business, and Bello's initial share represents 5/8 of the business.
Let's call the initial value of the business "V". Then, we can write:
3/8 V : 5/8 V = 3:5
To solve for V, we can cross-multiply and simplify:
(3/8)V x 5 = (5/8)V x 3
15/40 V = 15/40 V
V = V
So, the initial value of the business is V.
Now, let's consider what happens when Yakubu sells 3/4 of his share to Bello for N180000.
Since Yakubu initially owned 3/8 of the business, he sold 3/4 x 3/8 = 9/32 of the business to Bello.
After the sale, Yakubu now owns 3/8 - 9/32 = 3/32 of the business.
Bello now owns his initial share of 5/8 plus the 9/32 that he bought from Yakubu, which equals 45/32 of the business.
Since the entire business is now represented by Yakubu's remaining 3/32 share and Bello's 45/32 share, we can write:
3/32 V : 45/32 V = 3 : 45
To solve for V, we can cross-multiply and simplify:
(3/32)V x 45 = (45/32)V x 3
135/32 V = 135/32 V
V = V
Therefore, the value of the business is still V after the transaction. We just needed to find out what V was based on the initial ratio of Yakubu's and Bello's shares, which was given as 3:5.
Since the ratio of Yakubu's share to Bello's share is 3:5, this means that the total number of parts in the business is 3+5=8. Therefore, Yakubu's initial share represents 3/8 of the business, and Bello's initial share represents 5/8 of the business.
Let's call the initial value of the business "V". Then, we can write:
3/8 V : 5/8 V = 3:5
To solve for V, we can cross-multiply and simplify:
(3/8)V x 5 = (5/8)V x 3
15/40 V = 15/40 V
V = V
So, the initial value of the business is V.
Now, let's consider what happens when Yakubu sells 3/4 of his share to Bello for N180000.
Since Yakubu initially owned 3/8 of the business, he sold 3/4 x 3/8 = 9/32 of the business to Bello.
After the sale, Yakubu now owns 3/8 - 9/32 = 3/32 of the business.
Bello now owns his initial share of 5/8 plus the 9/32 that he bought from Yakubu, which equals 45/32 of the business.
Since the entire business is now represented by Yakubu's remaining 3/32 share and Bello's 45/32 share, we can write:
3/32 V : 45/32 V = 3 : 45
To solve for V, we can cross-multiply and simplify:
(3/32)V x 45 = (45/32)V x 3
135/32 V = 135/32 V
V = V
Therefore, the value of the business is still V after the transaction. We just needed to find out what V was based on the initial ratio of Yakubu's and Bello's shares, which was given as 3:5.