Question

A man sold two steel chairs for rs. 500 each. on one, he gains 20% and on other, he loses 12%. how much does he gain or lose in the whole transaction? 1.5% gain 2% gain 1.5% loss 2% loss

Answer 1

Given:

S.P. of the 1st chair =₹ 500

Gain = 20%


C.P. of the 1st chair = 100× s.p/(100+profit%)

= 500×100/(100+20)

=500×100/(120)= 50000/120= 5000/12= 1250/3

C.P. of the 1st chair =₹ 1250/3


S.P. of the 2nd chair = ₹ 500

Loss = 12%

C.P. of the 2nd chair =100× s.p/(100 - loss%)

= (500×100)/(100−12)

=500×100/(88)

=500×25/22

=250×25/11

=6250/11


C.P. of the 2nd chair = ₹ 6250/11


S.P. of both the chairs = 500 +500= ₹ 1000

C.P. of both the chairs= 1250/3 + 6250/11

= (13750+18750)/33

=32500/33


Net gain = 1000 – 32500 /33

=(33000- 32500)/ 33 = 500 /33

Net gain = 500/33

=Gain % =( gain / c.p ) × 100

= (500/33) × 100 /(32500/33)

=(500/32500)×100

= 50000/32500

= 500/325

= 100 /65

= 20/13

= 1.5%

Hence, he gain 1.5 % in the whole transaction.


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Hope this will help you...

Answer 2

The correct Answer is total gain = 1.5%

Solution:
The selling price of first chair is ₹500

Gain = 20%

We use the formula:
Sp= C.P (100+profit%)/100

C.P = S.Px100/(100+profit%)

C.P=500x100/(100+20)

=50000/120
=5000/12
= ₹250/3

C.P of first chair is ₹250/3
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Selling price of second chair = ₹500

Loss=12%

Formula used:
C.P= 100XS.P/(100-LOSS%)

C.P=100× 500/(100-12)
=50000/88
=₹ 6250/11

C.P of second chair is ₹ 6250/11
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S.P of both chairs = 500 + 500= ₹ 1000

C.p of both chairs = 1250/ 3 + 6250/11

By taking L.C.M
=(( 1250x11)+(6250x3))/33
=(13750+18750)/33
=32500/33

Net gain = S.P - C.P
=1000 - 32500/33
=(33000 - 32500)/33
=500/33

GAIN% = GAIN×100/ C.P
= (500/33)/(3250/33) ×100
=(500/3250) x100
=20/13
=1.5 %
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Therefore the gain% for the whole transactions is 1.5%