# 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)__

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

## Comments ( 9 )

Related Questions on Profit and Loss

A. 45 : 56

B. 45 : 51

C. 47 : 56

D. 47 : 51

A. Rs. 2600

B. Rs. 2700

C. Rs. 2800

D. Rs. 3000

A. A neither losses nor gains

B. A makes a profit of 11%

C. A makes a profit of 20%

D. B loses 20%

A. Rs. 3,750

B. Rs. 3,250

C. Rs. 2,750

D. Rs. 2,250

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

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

CP₁ : SP₁ = 20 : 23

CP₂ : SP₂ = 15 : 19.8

3.2 ≡ 20 ,Then 600 ≡ 3750

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)

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

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

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

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.

plzz explain how this new sp came in step 4