Question

17.
Ram sells a wrist watch to Mohan at 4% gain. Mohan sells the same watch to Sohan at 5% gain. If Seite
purchased this watch for 273, find the cost price of the watch for Ram.​

Answer 1

Answer:

Rs. 250

Step-by-step explanation:

$\displaystyle{ \mathfrak{ \pink{ \star \: Appropriate \: Question : }}}$

Ram sells a wrist watch to Mohan at 4% gain. Mohan sells the same watch to Sohan at 5% gain. If Sohan purchased this watch for 273, find the cost price of the watch for Ram.

$\displaystyle{ \mathfrak{ \pink{ \star \: Solution : }}}$

• Let the cost price of watch be Rs. x

$\sf{ \circ \: Ram \: sells \: to \: Mohan \: at \: 4 \% \: profit. }$

So,

$\displaystyle{ \leadsto \tt{x + x \times \frac{4}{100} }}$

$\displaystyle{ \tt{ \leadsto \: x + x \times \cancel{ \frac{4}{100}} }}$

$\displaystyle{ \tt{ \leadsto \: x + x \times \frac{1}{25} }}$

$\displaystyle{ \tt{ \leadsto \: x + \frac{x}{25} }}$

• Taking LCM

$\displaystyle{ \tt{ \leadsto \: \frac{25x + x}{25} }}$

$\displaystyle{ \tt{ \leadsto \: \frac{26x}{25} }}$

$\sf{S. P. \: of \: Ram \: and \: C. P. \: for \: Mohan \: = \dfrac{26x}{25} }$

Mohan sells at 5% gain.

So,

$\displaystyle{ \bf{ \mapsto \: \frac{26x}{25} + \frac{26x}{25} \times \frac{5}{100} }}$

$\displaystyle{ \bf{ \mapsto \: \frac{26x}{25} + \frac{26x}{25} \times \cancel{ \frac{5}{100} } }}$

• Took 26x/25 as common to make the calculations easier.

$\displaystyle{ \bf{ \mapsto \: \frac{26x}{25} \bigg \{1 + \frac{1}{20} \bigg \} }}$

$\displaystyle{ \bf{ \mapsto \: \frac{26x}{25} \bigg \{\frac{21}{20} \bigg \} }}$

Now,

$\sf{S. P. \: for \: Mohan \: \dfrac{26x}{25} \bigg \{ \dfrac{21}{20} \bigg \} }$

• Sohan purchased the watch for Rs. 273.

Solving the equation,

$\displaystyle{ \sf{ \implies \: \frac{26x}{25} \times \frac{21}{20} = 273 }}$

$\displaystyle{ \sf{ \implies \: x = 273 \times \frac{20}{21} \times \frac{25}{26} }}$

$\displaystyle{ \sf{ \implies \: x = \cancel{\frac{273 \times 20 \times 25}{21 \times 26} }}}$

$\displaystyle{ \sf{ \implies \: x = 250}}$

∴ Cost price for Ram is Rs. 250.

$\bf{ \star \:More \: Related \: Formulas : }$

$: \implies \displaystyle{ \boxed{ \tt{Loss\% = \frac{Loss}{C.P.} \times 100 }}}$

$: \implies \displaystyle{ \boxed{ \tt{Profit \% = \frac{Profit}{C.P.} \times 100 }}}$

$\displaystyle{ : \implies\boxed{ \tt{ \: Percentage \: Change = \frac{Actual \: Change}{ \: Original \: Amount} \times 100}}}$