» » » Uche, Adamu and Ope share profit on a business deal. Uche received $$\frac{1}{3}$$ of the profit and Adamu received $$\frac{2}{3}$$ of the remainder. If Ope recei...

# Uche, Adamu and Ope share profit on a business deal. Uche received $$\frac{1}{3}$$ of the profit and Adamu received $$\frac{2}{3}$$ of the remainder. If Ope recei...

### Question

Uche, Adamu and Ope share profit on a business deal. Uche received $$\frac{1}{3}$$ of the profit and Adamu received $$\frac{2}{3}$$ of the remainder. If Ope received the remaining ₦12,000, how much profit did they share?

A)
₦54,000
B)
₦58,000
C)
₦48,000
D)
₦42,000

## Discussion (3)

• Profit= a
Uche= 1/3 of a
Ope= remaining #12,000
Uche= 1/3 of a
=a/3
Adamu= 2/3 of remainder of a
= a -(1/3 of a)
=a/1 - a/3
= 3a - a/ 3
= 2a/3
Remainder of the profit= 2a /3
= 2/3 X 2a/3
Total profit = a/3 + 4a/9 +12000=a
12000= a/1 - a/3 - 4a/ 9
12000= 9a-3a-4a/ 9
12000= 2a/9
Cross multiply
12000 X 9 = 2a
108,000= 2a
Divide both sides by 2
2a/2 = 108,000/2
a= 54,000

• Profit= x
Uche= 1/3 of x
Ope= remaining #12,000
Uche= 1/3 of x
=x/3
Adamu= 2/3 of remainder of x
= x -(1/3 of x)
=x/1 - x/3
= 3x - x/ 3
= 2x/3
Remainder of the profit= 2x /3
= 2/3 X 2x/3
Total profit = x/3 + 4x/9 +12000=x
12000= x/1 - x/3 - 4x/ 9
12000= 9x-3x-4x / 9
12000= 2x/9
Cross multiply
12000 X 9 = 2x
108,000= 2x
Divide both sides by 2
2x/2 = 108,000/2
X= 54,000

1. Daniel

Pls remember that adamu did not receive 2/3 of the profit he received 2/3 of the remainder ,i.e when uche took 1/3 ,the remainder was 1-1/3 ,which is 2/3 so Adamu got 2/3 of 2/3 which is 4/9 and then Ope got 1-(1/3 +4/9) ,pls use this to solve and check it out