Question

You need a 18% acid solution for a certain test, but your supplier only ships a 13% solution and a 43% solution. You need 120 lts of the 18% acid solution. the 13% solution costs Rs 82 per ltr for the first 67 ltrs, and Rs 66 per ltr for any amount in excess of 67 liters. What is the cost of the 13% solution you should buy?

Answer 1

Since we need a 18% of solution for certain test.

But the supplier only ships a 13% solution and a 43% solution.

Therefore, let us assume that we need 'a' liters of 13% solution and 'b' liters of 43% solution which would be equivalent to requirement of 18% solution.

Therefore, $18=\frac{(a \times 13)+(b \times 43)}{a+b}$

Cross multiplying, we get

18a + 18b = 13a+43b

18a - 13a = 43b - 18b

5a = 25b

So, $\frac{a}{b}=\frac{5}{1}$

Since, he need 120 liters in total.

Therefore, 100 liters of 13% solution and 20 liters of 43% solution is needed.

Now, we have to find the cost of the 13% solution.

Since, the 13% solution costs Rs 82 per ltr for the first 67 ltrs, and Rs 66 per ltr for any amount in excess of 67 liters.

Therefore, total cost = $(67 \times 82)+(100-67) \times 66$

= 5494 + 2178

= 7672.

Therefore, the cost of the 13% solution is Rs 7672.