Question

A man purchased two baskets of fruits For Rs.1440.HE sold one basket at gain of 10percent and the othrer at 20percent gain and got an amount of Rs.1656.find the cost price of each basket of fruit.

Answer 1

Let the cost price of 1st basket be Rs `x` and 2hd basket be Rs `y`
GIven x +y = 1440 -------------------(1)
10% gain on 1st basket the price will be = x + (10/100) of x
                                                                 = x+10x/100
                                                                 = x + x/10
                                                                 = (10x +x)/10
                                                                 = 11x /10
20% gain on 2nd basket the price will be = y +(20/100) of y
                                                                  = y + 1/5 of y
                                                                  = y + y/5 
                                                                  = (5y +y) /5
                                                                  = 6y/5
Given that the total price = 1656 
⇒11x/10 + 6y/5 = 1656
 ⇒(11x + 12y)/10 = 1656
⇒ 11x +12y = 1656 ×10 
⇒11x + 12y =16560   --------------------------(2)
Subtracting 1 from 2
11x +12y = 16560
x + y = 1440

⇒11x +12y = 16560
 11(x + y = 1440)
  
⇒11x + 12y = 16560 
   11x + 11y =  15840
  -      -             -              [ signs changed for subtraction]
 0    +  y =  720
∴Cost of 2nd basket = y = Rs 720
Substitute y in eq 1, we get
x + y = 1440
⇒x + 720  = 1440
⇒x = 1440 - 720
∴x = 720
∴Cost of the 1st basket = Rs 720 and 2nd basket is also Rs720 

Answer 2

Let the 1st basket be cost price be 100x ( for some x )
=> Cost price of 2nd basket = 1440 - 100x

He sold 1st at gain of 10% => gain (1st) = 10% of 100x = 10x

He sold 2nd at a gain of 20% => gain (2nd) =
20% of ( 1440-100x) = 1/5 * (1440 - 100x ) = 288 - 20x

Net profit = 10x + 288 - 20x = 288 - 10x

But he made net profit = 1656 - 1440 = 216

=> 288 - 10x = 216 => x = ( 288 - 216 ) / 10 = 7.2

So cost price of 1st = 100x = 100 * 7.2 = ₹ 720
Cost price of 2nd = 1440 - 720 = ₹ 720