Question

The ratio in which tea costing rs 192 per kg is to be mixed with tea costing rs 150 per kg so that the mixed tea, when sold for rs 194.40 per kg, gives a profit of 20%, is ? Ans

Answer 1

$\sf{\underline{Answer:}}$ 2:5

$\sf{\underline{Given:}}$

Cost of price:

$\implies$ $\sf{\underline{First\:tea:}}$ Rs. 192 per kg.

$\implies$ $\sf{\underline{Second\:tea:}}$ Rs. 150 per kg.

$\sf{\underline{We\:know\:that:}}$

Mixture is to be sold in Rs.194.40 per kg.

$\sf{\underline{Note:}}$ + 20% profit.

$\sf{\underline{So:}}$

Selling price of Mixture = Rs.194.40 per kg.

$\sf{\underline{Now:}}$ Let the CP of Mixture be Rs. a per kg.

$\sf{\underline{Therefore:}}$

$\boxed{\sf{a + 20\% \: of \: a = Selling\:price}}$

$\huge\sf{ \frac{6a}{5} = 194.40}$

$\huge\sf{6a = 194.40 \times 5}$

$\huge\sf{6a = 972}$

$\huge\sf{a= \frac{972}{6} }$

$\boxed{\huge\sf{a= 162}}$

$\sf{\underline{So:}}$ $\sf{Rs.\:162 \: per \: kg}$

$\sf{\underline{Let:}}$

$\implies$ X kg of first tea.

$\implies$ Y kg of second tea to be added.

$\sf{\underline{Now:}}$

$\sf{What\:is\:Allegation?}$

$\bullet$ Allegation is a rule that enables us to find the ratio.

$\bullet$ In which two ingredients at the given price must be mixed.

$\bullet$ In order to produce a mixture of desired price.

Using Allegation, we get:

$\sf{\underline{Note:}}$ Check this attachment.

$\sf{\underline{Thus:}}$

$\huge\sf{ \frac{X}{Y} = \frac{162 - 150}{192 - 162}}$

$\huge\sf{ \frac{X}{Y} = \frac{12}{30} }$

$\huge\sf{ \frac{X}{Y} = \frac{2}{5}}$

$\boxed{\huge\sf{X:Y = 2:5} }$