Suresh started a shop with a capital of 19,200. He paid a loss of 5% in the first year but he gained a profit of 10% and 25/2% in the second and third year respectively. What was his total profit or loss at the end of third year?
Answers
GIVEN EQUATION IS
\bold{\boxed{\boxed{ ❲\frac{4x - 3}{2x + 1}❳ - 10 (\frac{2x + 1}{4x - 3} ) = 3}}}
❲
2x+1
4x−3
❳−10(
4x−3
2x+1
)=3
❲ 2x+14x−3 ❳−10( 4x−3 2x+1)=3❲2x+14x−3❳−10(4x−32x+1)=3
\bold{( \frac{4x - 3}{2x + 1} ) - 10 (\frac{2x + 1}{4x - 3} ) = 3} < /p > < p > ⟹( 2x+14x−3)−10( 4x−32x+1 )=3(
2x+1
4x−3
)−10(
4x−3
2x+1
)=3</p><p>⟹(2x+14x−3)−10(4x−32x+1)=3
⟹\bold{\frac{ {(4x - 3)}^{2} - 10 {(2x + 1)}^{2} }{(2x + 1)(4x - 3)} = 3}⟹ (2x+1)(4x−3)(4x−3) 2−10(2x+1) 2 =3
(2x+1)(4x−3)
(4x−3)
2
−10(2x+1)
2
=3⟹(2x+1)(4x−3)(4x−3)2−10(2x+1)2=3
\bold⟹(16 {x}^{2} - 24x + 9) - 10(4 {x^{2} + 4x + 1)}⟹(16x
2
−24x+9)−10(4x
2
+4x+1)
⟹(16x 2 −24x+9)−10(4x2 +4x+1)⟹(16x2−24x+9)−10(4x2+4x+1)
\bold{= 3(8 {x}^{2} - 6x + 4x - 3)}=3(8x < /p > < p > 2−6x+4x−3)=3(8x
2
−6x+4x−3)=3(8x</p><p>2−6x+4x−3)
\bold{16 {x}^{2} - 24x + 9 - 40 {x}^{2} - 40x - 10}16x 2 −24x+9−40x 2−40x−1016x
2
−24x+9−40x
2
−40x−1016x2−24x+9−40x2−40x−10
\bold{ = 24 {x}^{2} - 18x + 12x - 9}=24x < /p > < p > 2−18x+12x−9=24x
2
−18x+12x−9=24x</p><p>2−18x+12x−9
\bold{⟹- 24 {x}^{2} - 64x - 1 = 24 {x}^{2} - 6x - 9}⟹−24x 2 −64x−1=24x 2 −6x−9⟹−24x
2
−64x−1=24x
2
−6x−9⟹−24x2−64x−1=24x2−6x−9
⟹\bold{- 24 {x}^{2} - 24 {x}^{2} - 64x + 6x - 1 + 9 = 0}⟹−24x 2−24x 2−64x+6x−1+9=0⟹−24x
2
−24x
2
−64x+6x−1+9=0⟹−24x2−24x2−64x+6x−1+9=0
⟹\bold{- 48 {x}^{2} - 58x + 8 = 0}⟹−48x
2
−58x+8=0
⟹−48x 2−58x+8=0⟹−48x2−58x+8=0
⟹\bold{24 {x}^{2} + 29x - 4 = 0}⟹24x < /p > < p > 2+29x−4=0⟹24x
2
+29x−4=0⟹24x</p><p>2+29x−4=0
⟹\bold{24 {x}^{2} + 32x - 3x - 4 = 0}⟹24x
2
+32x−3x−4=0
⟹24x 2 +32x−3x−4=0
⟹\bold{8x(3x + 4) - 1(3x + 4) = 0}⟹8x(3x+4)−1(3x+4)=0
⟹8x(3x+4)−1(3x+4)=0
⟹\bold{(3x + 4)(8x - 1) = 0}⟹(3x+4)(8x−1)=0
⟹(3x+4)(8x−1)=0
⟹\bold{3x + 4 = 0}⟹3x+4=0⟹3x+4=0⟹3x+4=0
⟹\bold{8x - 1 = 0}⟹8x−1=0⟹8x−1=0⟹8x−1=0
\bold{\boxed{\red{x = - \frac{4}{3} }}}
x=−
3
4
x=−3/4