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A person sold a horse at a gain of 15%. Had he bought it for 25% less and sold it for Rs. 600 less, he would have made a profit of 32%. The cost price of the horse was:

A. Rs. 3,750

B. Rs. 3,250

C. Rs. 2,750

D. Rs. 2,250

Answer: Option A

Solution(By Examveda Team)

$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{original}}\,{\text{CP}} = {\text{Rs}}.\,X \cr & {\text{Hence}}, \cr & {\text{SP}} = X + 15\% \,{\text{of}}\,X \cr & \,\,\,\,\,\,\,\,\, = \frac{{115X}}{{100}} \cr & \,\,\,\,\,\,\,\,\, = Rs.\,\frac{{23x}}{{20}} \cr & {\text{New}}\,{\text{CP}} = x - 25\% \,{\text{of}}\,X \cr & = \frac{{75x}}{{100}} = \frac{{3x}}{4} \cr & {\text{New}}\,{\text{SP}} = \frac{{3x}}{4} + 32\% \,{\text{of}}\,\frac{{3x}}{4} \cr & = Rs.\,\frac{{99x}}{{100}} \cr & \cr & {\text{According}}\,{\text{to}}\,{\text{the}}\,{\text{question,}} \cr & {\frac{{23x}}{{20}}} - {\frac{{99x}}{{100}}} = 600 \cr & {\text{Or}},\,\frac{{ {115x - 99x} }}{{100}} = 600 \cr & 16x = 600 \times 100 \cr & X = 600 \times \frac{{100}}{{16}} \cr & \,\,\,\,\,\, = Rs.\,3750 \cr} $$

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Comments ( 9 )

  1. Mechanical Nitin
    Mechanical Nitin :
    3 months ago

    Cp(let)100__100+15____115%(sp1)
    Sp 100-25=75
    Profit %32 nikalna ha ok
    75×32÷100=24
    New sp2- 75+24=99
    115-99=16p
    16p-600
    600÷16×100=3750

    New

  2. Tarun Singh
    Tarun Singh :
    2 years ago

    OLD. NEW
    CP. 100. (100-25)=75
    Profit 15. 75*32/100=24
    SP. 115. 99
    Difference between old and new SP, 115-99=16
    Since, difference= 600
    Therefore. 16=600
    Now to calculate CP,
    (16/100)=(600/CP)
    CP= 3750

  3. Md Helal
    Md Helal :
    2 years ago

    CP₁ : SP₁ = 20 : 23
    CP₂ : SP₂ = 15 : 19.8
    3.2 ≡ 20 ,Then 600 ≡ 3750

  4. Abdullah All
    Abdullah All :
    2 years ago

    sp1 - sp2 = 600 ---------- (1)
    now let, cp = x
    sp1 = (115/100)x = 23x / 20
    new cp = (75/100)x = 3x/4
    so sp2 = (132/100)(3x/4) = 99x/100
    Now put the value eq(1)
    then x = 3750(ans)

  5. Likhan Mondol
    Likhan Mondol :
    2 years ago

    let, cp = 100
    sp = 115
    new cp = 75
    new sp = 75+ 75*(32/100)
    = 99
    sp difference = 115- 99 = 16
    Atq, when diff. 16 then cp = 100
    " " 1 " " = 100/16
    " " 600 " " = (100*600)/16
    = 3750

  6. Rakesh Kumar
    Rakesh Kumar :
    2 years ago

    It's very lengthy... Give short cut.plz.

  7. Piyush Sharma
    Piyush Sharma :
    3 years ago

    let CP=100x
    so SP=115x.
    now, according to question new CP=75x.
    new SP=115x-600.
    applying formula
    115x-600=132 /100 X 75x
    x=75/2.
    CP=100 X 75/2=3750

  8. Burada Balamurali
    Burada Balamurali :
    4 years ago

    1st condition
    let he purchased it for 100. therefore his selling price is 115
    2nd condition
    if he bought it for 25% less, means => let he bought it for 75 then his gain is 32%of 75= 24. => his selling price is 99

    C.P S.P
    100 115
    75 99

    difference b/w S.P is 115-99= 16

    c.p difference
    100 16
    ? 600

    cross multiply this and the answer is 3750.

  9. Sheena Khanna
    Sheena Khanna :
    5 years ago

    plzz explain how this new sp came in step 4

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