Question

How many kilograms of tea worth Rs300 per kg should be mixed with 10 kg of tea worth Rs240 per kg to produce a mixture to cost Rs260 per kg?

Answer 1

Hint: Here, let the amount of Rs300 per kg tea to be mixed be x. Therefore, 10kg of Rs240 per kg tea and $ x $ kg of Rs300 per kg tea will be used for the mixture to produce Rs260 per kg tea. Now, the sum of the rates of Rs300 per kg tea and Rs240 per kg tea must be equal to the rate of the mixture tea produced. Solve the equation, and we will get our answer.

Complete step-by-step answer:
In this question, we are given two different types of tea and their rate - Rs300 per kg and Rs240 per kg and we are asked to find the amount of tea to be mixed so that we can get another type of tea that costs Rs260 per kg.
Here, let the amount of Rs300 per kg tea to be mixed be $ x $ kg.
Now, we are given that 10 kg of Rs240 per kg tea and $ x $ kg of Rs300 per kg tea is used for the mixture to produce Rs260 per kg tea. Therefore, mixture will be
 $ \Rightarrow $ Mixture of tea to produce Rs260 per kg tea $ = \left( {10 + x} \right)kg $
So now, the rate of the mixture produced must be equal to the sum of rates of both Rs300 per kg tea and Rs240 per kg tea. Therefore,
 $ \Rightarrow $ Rate of Rs300 per kg tea for $ x $ kg $ = 300x $
 $ \Rightarrow $ Rate of Rs240 per kg tea for 10kg $ = \left( {240} \right)\left( {10} \right) $
 $ \Rightarrow $ Rate of Rs260 per kg tea for $ \left( {10 + x} \right)kg = 260\left( {10 + x} \right) $
Therefore,
 $ \Rightarrow 300x + 2400 = 260\left( {10 + x} \right) $
Opening the bracket, we get
 $
   \Rightarrow 300x + 2400 = 2600 + 260x \\
   \Rightarrow 300x - 260x = 2600 - 2400 \\
   \Rightarrow 40x = 200 \\
   \Rightarrow x = 5 \;
  $
Hence, 5kg of Rs300 per kg tea must be used in the mixture along with 10kg of Rs240 per kg tea to produce tea worth Rs260 per kg.
So, the correct answer is “5 kg”.

Note: The most important part of this question is taking the sum of rates of Rs300 per kg and Rs240 per kg tea equal to the rate of the mixture tea produced. We can also cross check our answer. Here we got the answer as 5kg, so $ \left( {10 + 5} \right) = 15kg $ of mixture tea. Its rate will be $ \left( {15 \times 260} \right) = Rs3900 $ .
Now, let us calculate the rate of Rs300 per kg tea.
 $ \Rightarrow $ Rate of Rs300 per kg tea $ = \left( {300 \times 5} \right) = Rs1500 $
And the rate of Rs240 per kg tea will be
 $ \Rightarrow $ Rate of Rs240 per kg tea $ = \left( {240 \times 10} \right) = Rs2400 $
If we add both these, we get $ 2400 + 1500 = Rs3900 $ .
Hence, our answer is correct.