Question

average price of three varieties of rice is rs 55,if the prices are in ratio4:5:2 then what is price of cheapest variety? ​

Answer 1

$\bf \underline{ \underline{\maltese\:Given} }$

$\sf Average \: price \: of \: three \: varieties \: of \: rice \: is \: Rs. \: 55$

$\sf \implies The \: prices \: are \: in \: ratio \: 4:5:2$

$\bf \underline{ \underline{\maltese\:To \: find } }$

$\sf \implies Price \: of \: cheapest \: variety = \: ?$

$\bf \underline{ \underline{\maltese\:Solution } }$

$\sf The \: prices \: are \: in \: ratio \: 4:5:2 \: \ \: \: \: \: [GIVEN]$

$\sf \implies Sum \: of \: the \: total \: ratio = 4 + 5 + 2 = 11$

$\bf \underline{Now},$

$\sf{C ost \: of \: {1}^{st} \: variety \: of \: rice = \dfrac{4}{11} \times55 }$

$\sf{ \implies \cancel{\dfrac{4}{ {11} }\times {55} } } = 20$

$\sf Hence, \: cost \: of \: {1}^{st} \: variety \: of \: rice = \bf Rs. \: 20$

$\: \: \: \: \: \:$

$\sf{C ost \: of \: {2}^{nd} \: variety \: of \: rice = \dfrac{5}{11} \times55 }$

$\sf{ \implies \cancel{\dfrac{5}{ {11} }\times {55} } } = 25$

$\sf Hence, \: cost \: of \: {2}^{nd} \: variety \: of \: rice = \bf Rs. \: 25$

$\: \: \: \: \: \:$

$\sf{C ost \: of \: {3}^{rd} \: variety \: of \: rice = \dfrac{2}{11} \times55 }$

$\sf{ \implies \cancel{\dfrac{2}{ {11} }\times {55} } } = 10$

$\sf Hence, \: cost \: of \: {3}^{rd} \: variety \: of \: rice = \bf Rs. \: 10$

$\: \: \: \: \: \:$

The price of $\bf {3}^{rd}$ variety of rice is Rs. 10, which is smallest among all the three varieties of rice.

$\bf \underline{Therefore},$

$\sf \implies Price \: of \: cheapest \: variety = \bf Rs. \: 10$