Question

Diagonal AC of rhombus ABCD is equal to one of its side BC .Find all the angles of the rhombus. What quantity of sweets worth Rs.120 per kg must be mixed with 20 kg of butter worth Rs.150 per kg to produce a mixture worth Rs.144 per kg? Sahil bought a plpot for Rs.96000.He sold 2/5 of its at a loss of 5% .At what profit per cent should he sell the remaining part to get a profit of 10% on the whole?

Answer 1

In a Rhombus the diagonals are perpendicular to each other meeting at the center O.

In the triangle BOC, ∠O = 90°.
   Sin ∠OBC = OC / BC = (1/2 AC) / BC = 1/2
   so  ∠OBC = 30°
   so angle ∠ABC = 2 * 30° = 60°

Then ∠OCB = 90° - ∠OBC = 60°
   so  ∠DCB = 2 * 60° = 120°

The angles of Rhombus are 60 and 120 deg.
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Sweets

quantity of sweets of sweets worth 120/kg  = N kg
Total cost of mixture = 144 * (20 + N) Rs
                =  N * 120 + 20 * 150  Rs
  =>  24 N = 120
  =>  N = 5 kg        Answer
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Cost price = Rs 96,000
Profit desired = 10% of cost = Rs 9,600
Total revenue from sale of the entire plot = Rs 96,000+ 9,600 
           = Rs 105, 600

Money obtained from sales of 2/5th of plot = (100 -5)/100 * 96,000 * 2/5
      = Rs 36, 480
Revenue to be obtained from the remaining 3/5th of plot
      = 105, 600 - 36, 480
       = Rs 69,120

Actual Cost of the 3/5 th of the plot = 3/5 * 96,000 = Rs 57,600

Profit % for 3/5th of the plot
       = (69,120 - 57,600) / 57,600   * 100%
       = 11, 520 / 57,600  * 100 %
         = 20 %