Question

*EMERGENCY* A merchant mixes three kinds of mangoes costing $120, $X, and $200 per kg in the ratio 1:4:2 so that the resultant mixture when sold at $198 per kg, yeilds a profit of 20%. What is the value of X?

Answer 1

Given:

A merchant mixes three kinds of mangoes costing $120, $X, and $200 per kg in the ratio 1:4:2 so that the resultant mixture when sold at $198 per kg, yields a profit of 20%.

To find:

The value of X

Solution:

The S.P. of the per kg resultant mixture = $ 198

Profit = 20%

∴ The C.P. of the per kg resultant mixture is,

= $\frac{100}{100 + G\%}\times S.P.$

= $\frac{100 }{100+ 20}\times 198$

= $\frac{100 }{120}\times 198$

= $\bold{\ \:165}$ ...... (i)

Here we are given

The 3 varieties of mangoes are mixed in the ratio of 1:4:2 so, the total weight of the resultant mixture of mangoes = 1 + 4 + 2 = 7 kg

and

The per kg cost of each variety is $ 120, $ X & $ 200

∴ The total cost of all varieties i.e., 7 kg mangoes is,

= ($ 120) + (4 × $ X ) + (2 × $ 200)

= 120 + 4X + 400

and

∴ The cost of 1 kg of the resultant mixture of mangoes is,

= $\frac{[120\: +\: 4X \:+\: 400]}{7}$ ...... (ii)

Now, from (i) & (ii), we can write an equation as:

$165 = \frac{[120\: +\: 4X \:+\: 400]}{7}$

$\implies 1155 = 120\: +\: 4X \:+\: 400$

$\implies 1155 = 520\: +\: 4X$

$\implies 4X = 1155 - 520$

$\implies 4X = 635$

$\implies X = \frac{635}{4}$

$\implies \bold{X = \ \:158.75\:per\:kg}$

Thus, the value of X is $ 158.75 per kg.

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