Question

1. Raj sells a bike at 25 % gain to Ashok. Ashok sold it to Surinder at 10 % profit. If Surinder pays Rs. 88,000 for the bike. Find the CP of the bike for Raju..

2. A toy was sold for Rs. 2700 therefore gaining 12 1/7 %. Find the CP of the Toy..

Please help me in this Questions..

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Answer 1

Solution - 1

$\tt \sf \: Surinder \: pays \: Rs. 88,000 \: to \: Ashok.$

$\sf \: For \: Ashok$

$\sf \: SP \: = \: Rs. \: 88,000$

$\sf \: Gain \: = \: 10 \: \%$

$\sf \red{\: C.P \: = \: \dfrac{100}{(100 + gain \%)} \: \times \: S.P}$

$\sf \: = \: \dfrac{100}{110} \: \times \: 88,000$

$\sf \: C P \: of \: the \: bike \: for \: Ashok \: = \: Rs. \: 8000$

$\sf \: For \: Raj$

$\tt\green {\underline{S.P = Rs. 80,000} \: \: \: \: \: \: \: \: \: \: \underline{Gain = 25 \: \% }}$

$\sf \: CP \: = \: \dfrac{100}{(100 \times 25)} \: \times \: Rs. \: 80,000$

$\sf \: = \: \dfrac{100}{12 5} \: \times \: Rs. \: 80,000$

$\tt \: \red{\underline{CP = Rs. 64,000}}$

$\underline{ \boxed {\mathrm {\ \purple{ \bigstar \: \: Therefore, \: Raj \: bought \: the \: bike \: for \: Rs. \: 64000. \: \: \bigstar } }}}$

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Solution - 2

$\begin{gathered} \tt{Given}\begin{cases} \sf{S.P \: of \: the \: toy = Rs. \: 2700}\\\\\sf{Gain \: \% \: = \: 12 \: \dfrac{1}{2} \% \: = \: \dfrac{25}{2} \: \% }\end{cases}\\\\\end{gathered}$

$\begin{gathered} \tt{To \: find }\begin{cases} \sf{We \: have \: to \: find \: the \: C.P \: of \: the \: toy. }\end{cases}\\\\\end{gathered}$

$\sf \: \green \therefore \purple{{ C.P \: of \: the \: toy \: = }\: \red{ \dfrac{100}{100 \: + \: gain \% } \: \times \: S.P }}$

$\sf \: {{ = }\: \dfrac{100}{100 \: + \: \dfrac{25}{2} \% } \: \: \times \: \: Rs. 2700 }$

$\sf \: {{ = }\: \dfrac{100}{ \: \dfrac{ 200 \: + \: 25}{2} } \: \: \times \: \: Rs. 2700 }$

$\sf \: \: = \: \dfrac{2 \: \times \: 100}{225} \: \times \: Rs. 2700 \: = \: Rs. \: 2400$

$\sf \red {\longrightarrow \:\underline{C.P \: = \: Rs. \: 2400}} \:$