Question

a person sells 40 apples per rupee and incurs a loss of 4 percent .how many apples per rupee he has to sellto have a gain of 8 percent

Answer 1

a person selto have 8percent

Answer 2

sp of 40 apples = 1
so, sp of 1 apple = 1 / 40
since, loss = 4 %
let the cp of 1 apple be X .
then ( for one apple ) , sp = cp - loss
sp = cp - 4% of cp
1 / 40 = X - ( 4/100 ) of X
1 / 40 = X - ( 1 / 25 ) of X
1 / 40 = 24x / 25
x = 25 / ( 40 * 24 )
since cp of one apple = X = 25 / ( 40 * 24 )
now let y apples for 1 rupee should be sold to have a gain of 8%
so, sp of y apples = 1
sp of 1 apple = 1 / y
also sp of 1 apple = cp of 1 apple + gain
= x + 8% of X
= x + ( 8 / 100 ) of X
= 27x / 25
here X = 25 / ( 40 * 24 )
so , sp of 1 apple = 27x / 25 = 27 { 25 / ( 40 * 24 ) } / 25 = 27 / ( 40 * 24)
but we have find that sp of 1 apple = 1 / y
then, 1/ y = 27 / ( 40* 24)
y = ( 40 * 24 ) / 27
y = 960 / 27 = 320 / 9 apples
hence, 320 / 9 apples should be sold at the rate of 1 to have gain of 8 % .