Answer:
20 mangoes.
Step-by-step explanation:
Given:
Total number of mangoes, a trader bought = [tex]x[/tex]
A trader bought at the rate of 4 mangoes for 10 naira.
Five of the mangoes were bad.
He sold the remaining at the rate of 5 mangoes for 20 naira.
He made a gain of 10 naira
Question asked:
Total number of mangoes, a trader bought = [tex]x[/tex] = ?
Solution:
Unitary method
Cost price of 4 mangoes = 10 naira.
Cost price of 1 mango = [tex]\frac{10}{4}[/tex]
Cost price of [tex]x[/tex] mango = [tex]\frac{10}{4}\times x= \frac{5}{2} x[/tex]
As 5 of the mangoes were bad and he sold the remaining mangoes, then Total number of mangoes sold = [tex]x-5[/tex]
Sale price of 5 mangoes = 20 naira
Sale price of 1 mango = [tex]\frac{20}{5}[/tex]
Sale price [tex]x-5[/tex] of mango = [tex]\frac{20}{5}\times(x-5)=4(x-5)=4x-20[/tex]
Now, as we know,
[tex]Gain = Sale price - cost price[/tex]
[tex]10 = 4x-20 -\frac{5}{2} x\\ 10=4x-\frac{5}{2} x-20\\10=\frac{8x-5x}{2} -20[/tex]
[tex]10 =\frac{3x}{2} -20[/tex]
Adding both sides by 20
[tex]30=\frac{3x}{2}[/tex]
Multiplying both sides by 2
[tex]60 = 3x[/tex]
Dividing both sides by 3
[tex]x=20[/tex]
Therefore, total number of mangoes, a trader bought is 20.
