a merchant purchased a horse and a biggie for RS.1200.He sold the horse at 20 % p4fit and biggie at 30 % profit and gets overall profit of 25 5/6% . find the cost of the horse and buggy
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The cost of the horse and buggy are Rs 500 and Rs 600 respectively.
Let the cost price of horse be Rs x and the cost price of the buggy be Rs y.
Given, he sold the horse at 20% profit.
So, SP of horse = (100+20)% of CP
= 120% of Rs x
= Rs 1.2x
Again, he sold the buggy at 30% profit.
So, SP of buggy = (100+30)% of CP
= 130% of Rs y
= Rs 1.3y
Total CP = x + y, which is equal to Rs 1200
So, x + y = 1200 ...(1)
25 5/6% profit on total CP is equal to,
(100 + 155/6)% of Rs (x+y)
= 755/6 % of Rs (x+y)
= Rs 755(x+y)/600
This is equal to total SP = Rs (1.2x + 1.3y)
Thus, (755x + 755y)/600 = 1.2x + 1.3y
⇒ 755x + 755y = 720x + 780y
⇒ 35x - 25y = 0
⇒ x = 5y/7
Putting this value in eqn. (1),
5y/7 + y = 1200
⇒ 12y = 8400
⇒ y = 8400/12 = 700 (Cost Price of buggy)
x = 5y/7 = 5*700/7 = 500 (Cost Price of horse)
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