Question

If one type of rice of cost Rs. 13.84 is mixed with another type of rice of cost Rs. 15.54. The mixture is sold at Rs. 17.6 with a profit of 14.6% on selling price then in which proportion the two types of rice mixed?
a)3:7
b)5:7
c)7:9
(d) None of these​

Answer 1

Answer:

Assume the amount of mixture were 100 units, maybe pounds, kilograms, stones, ounces, bushels, or whatever. Here, it is just being called "units". There becomes 100 units of mixture at Rs 15.0304 per unit, PRICE. This is the price WITHOUT counting the profit.

x, amount of the Rs 13.84 per unit rice

y, amount of the Rs 15.54 per unit rice

system%28%2813.84x%2B15.54y%29%2F100=15.0304%2Cx%2By=100%29

That is the system to solve, and you can then focus attention on the ratio of x and y. To make the work a little easier, take the mass or quantity sum equation and solve for either variable in terms of the other and substitute into the price equation and then solve for the single variable.

y=100-x

-

13.84x%2B15.54%28100-x%29=100%2A15.0304

13.84x%2B1554-15.54x=1503.04

%2813.84-15.54%29x=1503.04-1554

x=%281554-1503.04%29%2F%2815.54-13.84%29

x=50.96%2F1.7

highlight%28x=29.98%29

Answer 2

Answer:

The correct option is: a)3 : 7

Step-by-step explanation:

• Suppose 'x' gm of rice of cost Rs. 13.84 is mixed with 'y' gm of rice of cost Rs. 15.54.

      Total cost price = 13.84x + 15.54y

      Total amount of rice (x + y) is sold at a rate of Rs. 17.6

      Total selling price = 17.6(x + y)

      Profit = 17.6(x + y) - 13.84x + 15.54y = 3.76x + 2.06y

      Profit percentage on selling price = $\frac{profit}{selling price} \times$ 100%

                                                               =  $\frac{3.76x + 2.06y}{17.6x + 17.6y}$ × 100%

• The given profit percentage = 14.6%

      We can write,   $\frac{3.76x + 2.06y}{17.6x + 17.6y}$ × 100% = 14.6%

                              $\frac{3.76x + 2.06y}{17.6x + 17.6y}$ × 100 = 14.6

                             100(3.76x + 2.06y) = 14.6 × 17.6(x + y)

                             376x + 206y = 256.96x + 256.96y

                             376x - 256.96x = 256.96y - 206y

                              119.04x = 50.96y

                               119x = 51y                [119.04 ≈ 119 and 50.96 ≈ 51]

                              $\frac{x}{y} = \frac{51}{119} = \frac{3}{7}$

                            x : y = 3 : 7

  ∴ Two rice are mixed in a proportion of 3 : 7.

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