For Example:

(Q) A trader bought two watches for Rs 2300. He sold one at a profit of 10% and the other at a profit of 20%. If the selling price of each watch is the same, then their cost price are respectively.

Solution: By Trick:

C.P of watch at a profit of 10%=((100+20)/(200+10+20))×2300

                                     =(120/230)×2300

=Rs 1200 Ans.

C.P of watch at a profit of 20%=Rs(2300-1200)

                                                             =Rs 1100 Ans.

BY CONCEPT:

Let C.P of 1st watch=x

C.P of 2nd watch=2300-x

S.P of 1st watch:

x×(100+10)/100=S.P1

11x/10=S.P1

S.P of 2nd watch:

(2300-x)×(100+20)/100=S.P2

(2300-x)×120/100=S.P2

(2300-x)×12/10=S.P2

Now According to question: selling price of each watch is the same

SO,

S.P1=S.P2

11x/10=(2300-x)×12/10

11x=2300×12-12x

23x=2300×12

x=Rs 1200 Ans

C.P of 2nd watch=2300-x

=Rs(2300-1200)

=Rs 1100 Ans.

 

If two article are sold at equal prices, the first one is sold at a Loss of L1% and whereas the second one at a Loss of L2%, And the sum of the cost price of two article is x then

For Example:

(Q) A Man purchases two T.V sets for Rs 21,500. He sold one at a Loss of 12% and the other at a loss of  16%. If the selling price of each T.V is the same, then their cost price are respectively.

Solution: By Trick:

C.P of T.V at a Loss of 12%=((100-16)/(200-12-16))×21500

                                                    =(84/172)×21500

                                                    =Rs 10500 Ans.

C.P of T.V at a Loss of 16%=Rs(21500-10500)

                                                     =Rs 11000 Ans.

BY CONCEPT:

Let C.P of 1st T.V =x

C.P of 2nd T.V=21500-x

S.P of 1st T.V:

x×(100-12)/100=S.P1

88x/100=S.P1

S.P of 2nd T.V:

(21500-x)×(100-16)/100=S.P2

(21500-x)×84/100=S.P2

(21500-x)×84/100=S.P2

Now According to question: selling price of each T.V is the same

SO,

S.P1=S.P2

88x/100=(21500-x)×84/100

88x=21500×84-84x

172x=21500×84

x=Rs 1o500 Ans

C.P of 2nd T.V=21500-x

=Rs(21500-10500)

=Rs 11000 Ans.

 

If two article are sold at equal prices, the first one is sold at a Profit of P% and whereas the second one at a Loss of L%, And the sum of the cost price of two article is x then

For Example:

(Q) A Man purchases two horses for Rs 16,800. He sold one at a Profit of 25% and the other at a loss of  15%. If the selling price of each horse is the same, then their cost price are respectively.

Solution: By Trick:

C.P of horse at a profit of 25%=((100-15)/(200+25-15))×16800

                                                 =(85/210)×16800

                                                 =(85/210)×16800

                                                 =Rs 6800 Ans.

C.P of horse at a Loss of 15%=Rs(16800-6800)

                                                        = Rs 10000 Ans.

BY CONCEPT:

Let C.P of 1st horse=x

C.P of 2nd horse=16800-x

S.P of 1st horse:

x×(100+25)/100=S.P1

125x/100=S.P1

S.P of 2nd horse:

(16800-x)×(100-15)/100=S.P2

(16800-x)×85/100=S.P2

(16800-x)×85/100=S.P2

Now According to question: selling price of each horse is the same

SO,

S.P1=S.P2

125x/100=(16800-x)×85/100

125x=16800×85-85x

210x=16800×85

x=Rs 6800 Ans

C.P of 2nd horse=16800-x

=Rs(16800-6800)

=Rs 10000 Ans.

 

If two article are sold at equal prices, the first one is sold at a Loss of L% and whereas the second one at a Profit of P%, And the sum of the cost price of two article is x then

For Example:

(Q) A trader bought two horses for Rs 19,500. He sold one at a Loss of 20% and the other at a Profit of  15%. If the selling price of each horse is the same, then their cost price are respectively.

Solution: By Trick:

C.P of horse at a Loss of 20%=((100+15)/(200-20+15))×19500

                                               =(115/195)×19500

                                               =Rs 11500 Ans.

C.P of horse at a Profit of 15%=Rs(19500-11500)

                                                           =Rs 8000 Ans.

The common and frequently asked problem of Profit and Loss question with solution and Shortcut Tricks for Bank PO, SSC CGL, SSC CHSL, Railway Exam Type-4.1.