Question

please help me ..solve this ​

Answer 1

Problem:-

• If the manufacturer gains 6%, the wholesale dealer 8% and the retailer 10%, then what is the production cost of a geyser whose retail price is ₹ 15741?

Solution:-

$\sf ✰Let \: the \: production \: cost \: of \: the \: geyser \: be \: ₹x.$

$\sf Manufacturer's \: gain \: = \: 6%$

✰ $\sf SP \: of \: manufacturer \: = \: 106% \: of \: ₹x$

= ₹ [x × $\sf\dfrac{106}{100}$ = ₹ $\sf\dfrac{53x}{50}$

$\sf Wholesale \: dealer's \: gain \: = \: 8%$

$\sf SP \: of \: dealer \: = \: 108% \: of \: ₹ [tex]\sf\dfrac{53x}{50}$

$\implies₹\mathtt{\dfrac{53x}{50}} \times \mathtt{\dfrac{108}{100}} = ₹\mathtt{\dfrac{53x}{50}} \times \mathtt{\dfrac{27}{25}}$

$\sf Retailer's \: gain \: = \: 10%$

$\sf SP \: of \: the \: retailer \: = \: 110% of ₹ [tex]\sf\dfrac{53x}{50}$ × $\sf\dfrac{27}{25}$

= ₹ $\sf\dfrac{53x}{50}$ × $\sf\dfrac{27}{25}$ × $\sf\dfrac{110}{100}$ = ₹ $\sf\dfrac{53x}{50}$× $\sf\dfrac{27}{25}$ × $\sf\dfrac{11}{10}$

$\sf But \: the \: retail \: price \: is \: ₹15741$.

✰ $\sf\dfrac{53x}{50}$ × $\sf\dfrac{27}{25}$ × $\sf\dfrac{11}{10}$ = $\sf 15741$.

= $\sf\dfrac{15741×50×25×10}{53×25×10}$ = 12500

Hence, the cost of production of the geyser is ₹ 12500.

____________________________

Answer 2

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$\sf Let \: the \: production \: cost \: of \: the \: geyser \: be \: ₹x.$

$\sf Manufacturer's \: gain \: = \: 6%$

$\sf SP \: of \: manufacturer \: = \: 106% \: of \: ₹x$

$\sf\implies$ ₹ [x × $\sf\dfrac{106}{100}$ = ₹ $\sf\dfrac{53x}{50}$

$\sf Wholesale \: dealer's \: gain \: = \: 8%$

$\sf SP \: of \: dealer \: = \: 108% \: of \: ₹ [tex]\sf\dfrac{53x}{50}$

$\implies₹\mathtt{\dfrac{53x}{50}} \times \mathtt{\dfrac{108}{100}} = ₹\mathtt{\dfrac{53x}{50}} \times \mathtt{\dfrac{27}{25}}$

$\sf Retailer's \: gain \: = \: 10%$

$\sf SP \: of \: the \: retailer \: = \: 110% of ₹ [tex]\sf\dfrac{53x}{50}$ × $\sf\dfrac{27}{25}$

$\sf\implies$ ₹ $\sf\dfrac{53x}{50}$ × $\sf\dfrac{27}{25}$ × $\sf\dfrac{110}{100}$ = ₹ $\sf\dfrac{53x}{50}$× $\sf\dfrac{27}{25}$ × $\sf\dfrac{11}{10}$

$\sf But \: the \: retail \: price \: is \: ₹15741$.

$\sf\dfrac{53x}{50}$ × $\sf\dfrac{27}{25}$ × $\sf\dfrac{11}{10}$ = $\sf 15741$.

$\sf\implies$$\sf\dfrac{15741×50×25×10}{53×25×10}$ = 12500

Hence, the cost of production of the geyser is ₹ 12500.

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