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?
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.
To find the value of the business, you need to determine the total value of Yakubu's share before he sold 3/4 of it to Bello.
Let's assume Yakubu's share is represented by "x". Since the ratio of their shares is 3:5, Bello's share would be 5x.
Yakubu sold 3/4 of his share to Bello, which means he retained 1 - 3/4 = 1/4 of his original share after the sale.
The amount Yakubu received for selling 3/4 of his share is N180,000. So, the value of his original share (before the sale) must have been 4 times this amount, which is 4 * N180,000 = N720,000.
Since Bello's share was 5 times Yakubu's share, Bello's share in the business had a value of 5 * N720,000 = N3,600,000.
To find the total value of the business, you add the values of Yakubu's and Bello's share:
Total value = Value of Yakubu's share + Value of Bello's share
= N720,000 + N3,600,000
= N4,320,000
Therefore, the value of the business is N4,320,000.