Question

Ques.-1) Kiki sells a book to Lily at a loss of 5% and Lily sells it to Riya at a loss of 10% . If Riya pays Rs 855 for the book , at what price was the book bought by Kiki ?

Ques.-2) Simplify:-
• (-26) × 72 + (-26) × 28
• (-16) × (-18) + (-4) × (-8)​

Answer 1

$\sf \bf \huge {\boxed {\mathbb {QUESTION}}}$

$\tt 1:\:\: KiKi\: sells \:a \:book \:to\: Lily\: at\: a\: loss\: of\: 5\%\: and\: Lily\\\tt sells\: it\: to\: Riya\: at \:a\: loss\: of\: 10\%.\: If \:Riya\: pays\\\tt Rs\: 855 \:for \:the\: book,\: at\: what\: price\: was \:the\\\tt book\: bought\: by\: KiKi?$

$\sf \bf \huge {\boxed {\mathbb {ANSWER}}}$

$\sf \bf {\boxed {\mathbb {GIVEN}}}$

• $\bf KiKi \:sells\: a \:book\: to\: Lily \:at \:a\: loss=5\%$
• $\bf Lily \:sells\: a \:book\: to\: Riya \:at \:a\: loss=10\%$
• $\bf The\: price\: of\: the\: book\:bought\: by\:Riya =Rs \:855$

$\sf \bf {\boxed {\mathbb {TO\:FIND}}}$

• $\bf Cost price of the book bought by KiKi$

$\sf \bf {\boxed {\mathbb {SOLUTION}}}$

${\pink {\underline {\pmb {\bf {The\: price\: of\: the\: book\:bought\: by\:Lily}}}}}$

${\blue {\boxed {\boxed {\boxed {\green{\pmb {CP=\dfrac{100}{100-L\%}\times SP}}}}}}}$

• $\sf CP=cost\:price\:of\:the\:book\:sold\:by\:Lily$
• $\sf L=loss\: percentage\:of\: the\: book\: sold\: by\: Lily$
• $\sf SP=selling \:price\:of\:the \:book$

${\underbrace {\overbrace {\orange {\pmb {Substitute \:the \:values}}}}}$

$\bf \implies CP=\dfrac{100}{100-10}\times 855$

$\bf \implies CP=\dfrac{100}{90}\times 855$

$\bf \implies CP=\dfrac{10\cancel{0}} {9\cancel{0}}\times 855$

$\bf \implies CP=\dfrac{100}{\cancel{9}}\times \cancel{855}$

$\bf \implies CP=100\times 95$

$\implies {\blue {\boxed {\boxed {\purple {\sf {CP=950}}}}}}$

—————————————————————————————

${\pink {\underline {\pmb {\bf {The\: price\: of\: the\: book\:bought\: by\:Kiki}}}}}$

${\blue {\boxed {\boxed {\boxed {\green{\pmb {CP=\dfrac{100}{100-L\%}\times SP}}}}}}}$

• $\sf CP=cost\:price\:of\:the\:book\:sold\:by\:Kiki$
• $\sf L=loss\: percentage\:of\: the\: book\: sold\: by\: Kiki$
• $\sf SP=selling \:price\:of\:the \:book$

${\underbrace {\overbrace {\orange {\pmb {Substitute \:the \:values}}}}}$

$\bf \implies CP=\dfrac{100}{100-5}\times 950$

$\bf \implies CP=\dfrac{100}{95}\times 950$

$\bf \implies CP=\dfrac{100}{\cancel{95}}\times \cancel{950}$

$\bf \implies CP=100\times 10$

$\implies {\blue {\boxed {\boxed {\purple {\mathfrak {CP=1000}}}}}}$

${\underbrace {\red {\overline {\red {\underline {\red {\pmb {\sf {{\therefore}} The\: price\: of\: the\: book\:bought\: by\:Kiki\:is\:Rs\:1000}}}}}}}}$

__________________________________________

$\sf \bf \huge {\boxed {\mathbb {QUESTION}}}$

$\tt 2: Simplify :-$

• ${\tt{ ( - 26 ) \times 72 + ( - 26 ) \times 28 }}$

• ${\tt{ ( - 16 ) \times ( - 18 ) \:+\: ( - 4 ) \times ( - 8 ) }}$

$\sf \bf {\boxed {\mathbb {SOLUTIONS}}}$

$\longrightarrow {\bf{ ( - 26 ) \times 72 + ( - 26 ) \times 28 }}$

$\bf \implies (-1872)+(-7 2 8)$

$\implies {\blue {\boxed {\boxed {\purple {\mathfrak {-2600}}}}}}$

—————————————————————————————

$\longrightarrow {\bf{ ( - 16 ) \times ( - 18 ) \:+\: ( - 4 ) \times ( - 8 ) }}$

$\bf \implies 288 +31$

$\implies {\blue {\boxed {\boxed {\purple {\mathfrak {320}}}}}}$

__________________________________________

$\sf \bf \huge {\boxed {\mathbb {EXTRA\:INFORMATION}}}$

$\sf Gain\%=\dfrac{gain\times 100}{CP}$

$\sf Loss\%=\dfrac{loss\times 100}{CP}$

$\sf Selling \:price=\dfrac{100-L\%}{100}\times CP$

$\sf Selling \:price=\dfrac{100+P\%}{100}\times CP$

$\sf Cost\: price =\dfrac{100}{100-L\%}\times SP$

$\sf Cost \:price =\dfrac{100}{100+P\%}\times SP$