Question

a tape recordee is sold 2760 at a gain of 15% and cd player is sold for 3240 at loss of 10%
1.find cp of tap recorder

2.cp of the CD player
3.the total cp of both
4 the total sp of both
gain and lose %​

Answer 1

Case-1:

S.P. of the recorder = 2760

Gain = 15%

Let, the C.P. of the recorder be, 'y'

∴ Gain = (y*15/100)

           = 3y/20

By condition,

y+(3y/20) = 2760

⇒ (20y+3y)/20=2760

⇒ 23y = 2760*20

⇒ y = 55200/23

⇒ y = 2400

∴ The C.P. of the recorder is 2400

Case-2:

S.P. of the CD player = 3240

Loss = 10%

Let, the C.P. of the CD player be, 'x'

∴ Loss = (x*10/100)

            = x/10

By condition,

x-(x/10) = 3240

⇒(10x-x)/10 = 3240

⇒ 9x = 3240*10

⇒ x = 32400/9

⇒ x = 3600

So, the C.P. of the CD player is 3600

Case-3:

C.P. of the recorder is 2400

C.P. of the CD player is 3600

∴ The total C.P. is = (2400+3600)

                             = 6000

So, both costs together 6000

Case-4:

The S.P. of the recorder is 2760

The S.P. of the CD player is 3240

∴ The total S.P. is (2760+3240)

                             = 6000

So, the total S.P. is 6000.

Seems the total S.P. is equal to that of Total C.P. Hence, there is no loss or gain.

Answer 2

Answer:

In the case of the first tape – recorder :

S.P. = Rs. 990

Gain = 10%

C.P. = 100/(100 + gain%) × S.P.

= 100/(100 + 10) × Rs. 990 = Rs. 100/110 × 990

= Rs. 100 × 9 = Rs. 900

In the case of second tape – recorder :

S.P.  = Rs. 990

Loss = 10%

C.P. = 100/(100 – Loss%) × S.P.

= 100/ (100 – 10) × Rs. 990 = 100/90 × 990

= 100 × 11 = Rs. 1100  

Total C.P. of both the tape–recorders

= Rs. 900 + Rs. 1100 = Rs. 2000

Total S.P. of both the tape–recorders

= Rs. 990 + Rs. 990 = Rs. 1980

Loss on the whole transaction

= C.P. – S.P. = Rs. 2000 – Rs. 1980

= Rs. 20

Loss % = Loss/C.P. × 100

= Rs. 20/Rs. 2000 × 100 = 2/2 % = 1%

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