**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?### Options

A)

₦54,000

B)

₦58,000

C)

₦48,000

D)

₦42,000

The correct answer is A.

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## Discussion (3)

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Profit= a

Uche= 1/3 of a

Adamu= 2/3 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

Adamu = 2/3 of 2a/3

= 2/3 X 2a/3

Adamu receives 4a/9

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

Adamu= 2/3 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

Adamu = 2/3 of 2x/3

= 2/3 X 2x/3

Adamu receives 4x/9

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

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