Question

how many kilos of tea worth Rs. 72 per kg should be mixed with 10 kg of tea worth Rs. 90 per kg to produce a mixture , which will together cost Rs. 78 per kg ?

Answer 1

Given, 10kg of tea worth Rs 90 per kg is taken.

Let x kg of tea worth Rs 72 per kg is mixed with 10kg of tea worth Rs 90 per kg.

Now, total cost of Rs. 90 per kg quality tea = Rs 10 × 90 = Rs 900

and total cost of Rs. 72 per kg quality tea = Rs x × 72 = Rs 72x

After mixing total amount of Rs. 78 per kg quality tea obtained = (x + 10) kg

So, cost of tea obtained after mixing = Rs (x + 10) × 78 = Rs 78x + 780

Now, cost before mixing = cost after mixing

⇒ 72x + 900 = 78x + 780

⇒ 72x - 78x = 780 - 900

⇒ -6 x = -120

⇒ x = 20

Hence, 20 kg of tea worth Rs. 72 per kg should be mixed with 10 kg of tea worth Rs. 90 per kg to produce a mixture together costing Rs. 78 per kg.