Question

A trader bought x mangoes at the rate of 4 mangoes for 10 naira five of the mangoes were bad so he sold the remaining at the rate of 5 mangoes for 20 naira and he made a gain of 10 naira how many mangoes did he buy ?

Answer 1

Answer:

20 mangoes.

Step-by-step explanation:

Given:

Total  number of mangoes, a trader bought = $x$

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 = $x$ = ?

Solution:

Unitary method

Cost price of  4 mangoes =  10 naira.

Cost price of  1 mango = $\frac{10}{4}$

Cost price of $x$ mango = $\frac{10}{4}\times x= \frac{5}{2} x$

As 5 of the mangoes were bad and he sold the remaining mangoes, then Total number of mangoes sold =  $x-5$

Sale price of 5 mangoes = 20 naira

Sale price of 1 mango = $\frac{20}{5}$

Sale price $x-5$ of mango = $\frac{20}{5}\times(x-5)=4(x-5)=4x-20$

Now, as we know,

$Gain = Sale price - cost price$

$10 = 4x-20 -\frac{5}{2} x\\ 10=4x-\frac{5}{2} x-20\\10=\frac{8x-5x}{2} -20$

$10 =\frac{3x}{2} -20$

Adding both sides by 20

$30=\frac{3x}{2}$

Multiplying both sides by 2

$60 = 3x$

Dividing both sides by 3

$x=20$

Therefore, total number of mangoes, a trader bought is 20.