Question

by selling an article for Rs.220,
a man
loses 12./. At what rate must he sell so
as to gain 16./.​

Answer 1

$\large\looparrowright \pink{ \underline{ \underline{ \orange{ \rm \: given : }}}}$

• Selling price = rs 220

• loss% = 12%

• Wanted Gain% = 16%

$\large\looparrowright \purple{ \underline{ \underline{ \blue{ \rm \: to \: \: find : }}}}$

• The Selling price with gain of 16%

_____________________________________________

$\large\looparrowright \red{ \underline{ \underline{ \green{ \rm \:solution : }}}}$

$\mapsto$ Find out Cost price

• we know,

$\large \orange{ \boxed{ \boxed{ \purple{ \rm \: c.p = \frac{s.p \times 100}{100 - loss\%} }}}}$

$\implies \rm \: c.p = \dfrac{220 \times 100}{100 - 12}$

$\implies \rm \: { c.p = \dfrac{22000}{88} }$

$\large \therefore \red{ \boxed{ \blue{\rm \: cost \: price \: = rs. \: 250}}}$

• now,

$\large \orange{ \boxed{ \boxed{ \purple{ \rm \: profit = \frac{profit\% \times c.p}{100} }}}}$

$\implies \rm \: profit = \dfrac{16 \times 220}{100}$

$\implies \pink{ \rm \: profit = \dfrac{16 \times 22}{10} }$

$\implies \rm \: profit = \dfrac{352}{10}$

$\large \therefore \red{ \boxed{ \blue{\rm \: profit = rs. \: 35.2}}}$

$\dashrightarrow$ Now, we have profit on s.p of 16%

$\rightarrowtail$ New s.p with 16%profit = old s.p + profit

$\implies$ S.P = 220 + 35.2

$\large \: \: \: \: \: \: \: \therefore \pink{ \boxed{ \green{\rm \: s.p = rs \: \: 255.2}}}$

$\rightarrowtail$ Rate at which he must sell the aritical so as to gain 16% = rs 255.2