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Word Problem 4

Problem 4: A merchant bought one kind of teas at Rs 12 per kg and the second kind of tea at Rs 28 per kg. He mixed these and sold the mixture at Rs 32 per kg. If his gain percent is 28, the ratio of two kinds of teas is ;

a) 3:13                       b) 7:13                        c) 8:5                        d) 7:9

Solution:

 

The data is ;

Cost price of T1 = Rs 12 per kg

Cost price of T2 = Rs 28 per kg

Sale price of mixture = Rs 32 per kg

Prift = 28%

Ration between teas = T1:T2 = ?

 

We start by supposing that;

Cost price of mixture = Y Rs per kg

But he got 28% profit i-e 28% as extra  of mixture cost price !

so,

28% (profit ) of  cost price ;

\[ 28 Percent Profit= \frac{28}{100} \times Y \]

Since sale price is sum of cost price and profit ;

so,

\[ Sale Price = \frac{28}{100}\times Y+ Y \]

\[ = \frac{128Y}{100} \]

But sale price is Rs 32 so,

\[ \frac{128Y}{100} = 32 \]

This gives us;

\[ Y=\frac{32\times 100}{128}= Rs 25 \]

Thus cost price of mixture is Rs 25

Now we use blending formula;

 

Note: While using blending formula we subtract teas prices from the mixture and put the result accross two corssed lines as shown!

 

So, we got,

T1 : T2 = 3:13

i-e ratio is 3:13

 


 


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