# RD Sharma Solutions Class 8 Mathematics Solutions for Profit Loss Discount and Value Added Tax Exercise 13.1 in Chapter 13 - Profit Loss Discount and Value Added Tax

Question 18 Profit Loss Discount and Value Added Tax Exercise 13.1

Mariam bought two fans for Rs 3605. She sold one at a profit of 15% and theother at a loss of 9%. If Mariam obtained the same amount for each fan, find thecost price of each fan.

Given, cost price of 2 fans is = Rs 3605

Let cost price of 1 fan be = Rs x

Then CP of other fan will be = Rs 3605 – x

We know that one is a gain and other is a loss.

Selling price of first fan (gain) = x + x×15/100

= x + x×3/20

= (20x+3x)/20

= Rs 23x/20

Selling price of second fan (loss) = (3605 - x) × 91/100

= Rs (3605×91 – 91x)/100

So now, by equating both we get,

23x/20 = (3605×91 – 91x)/100

23x = (3605×91 – 91x)/5

23x × 5 = 3605×91 – 91x

115x + 91x = 3605×91

206x = 3605×91

x = (3605×91)/206

= 1592.50

∴ Cost price of one fan (x) is = Rs 1592.50

Cost price of second fan (3605 - x) is = 3605 – 1592.50 = Rs 2012.50

Video transcript
"hello students i am rita your master tutor and the today's question is maryam bought two fans for rupees 3605 she showed one or one at a profit of 15 percent and the other at the loss of nine percent if mariam obtained the same amount for each fan find the cost price of each fan first of all let cost price of first fan that is cpu one is equal to rupees x then the cost price of second fan will become rupees 3605 minus x okay and in the first one he she got a profit of 15 percent and the second one she got a loss of nine percent okay so first of all we find the sp1 setting price of first fan is 100 plus probably put the formula of sp 100 plus profit percent divided by 100 into cp cp is x so it becomes so sp1 is equal to 100 plus 15 that is 115 by 100 x this is our sp1 now we find the sp2 100 minus loss percent divided by 100 into cp2 cp2 is 3605 minus x so sp2 is equal to 100 minus 991 by 100 3605 minus x but in the question it is given that the selling price is same of for each fan then according to question it is given that sp1 is equal to sp2 now we solve this equation sp1 is equal to sp true now we solve the equation as p1 is 115 by 100x is equal to sp2 is 91 by 100 bracket 3605 minus x now we solve this 100 cancel out each other so 115 x is equal to 91 into 3 605 minus 91 x so 115 x plus 91 x is equal to 91 into 3 600 5 and when we add these two then it becomes 206x is equal to 91 into 3 605 then it becomes 3 2 8 0 double 5 now the value of x when we divide this 3 2 8 0 double divided by 206 then the value of x is equal to rupees 1592.50 peso so this is the cp of first fan is equal to rupees one five nine two point five zero then the cp of second one is equal to rupees three thousand six hundred five minus one thousand five hundred ninety two point fifty then we got rupees two thousand twelve point fifty so this is our answer i hope you like this video so please subscribe leader for more updates and do comment your questions thank you"
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