(a) A manufacturing company requires 3 hours of direct labour to process N87.00 worth of raw materials. If the company uses N30,450.00 worth of raw materials, what amount should it budget at N18.25 per hour?
(b) An investor invested Nx in bank M at the rate of 6% simple interest per annum and Ny in bank N at the rate of 8% simple interest per annum. If a total of N8,000,000.00 was invested in the two banks and the investor received a total of N2,320,000.00 as interest from the two banks after 4 years, calculate the:
(i) values of x and y
(ii) interest paid by the second bank.
Explanation
(a) Worth of raw materials = N30,450.00
Worth of raw material to get processed materials = N87.00
Amount of raw material to get processed material = \(\frac{30,450}{87}\)
Time required for direct labour = 3 hours
Amount that will be budgeted for direct labour at N18.25 per hour =
\(3 \times 18.25 \times \frac{30,450}{87}\)
= \(\frac{1667137.5}{87}\)
= N19,162.50
(b) Total amount invested \(N(x + y) = N8,000,000 ....(1)\)
Interest from bank M = \(\frac{x \times 4 \times 6}{100} = 0.24x\)
Interest from bank N = \(\frac{y \times 4 \times 8}{100} = 0.32y\)
\(0.24x + 0.32y = 2,320,000 .... (2)\)
(i) Multiplying (1) by 0.24 in order to eliminate x, we have
\(0.24(x + y) = 0.24(8,000,000.00)\)
\(0.24x + 0.24y = 1,920,000.00 .... (3)\)
(2) - (3) : \(0.32y - 0.24y = 2,320,000 - 1,920,000 = 400,000\)
\(0.08y = 400,000 \implies y = \frac{400,000}{0.08} = N5,000,000\)
\(x = 8,000,000 - y\)
= \(8,000,000 - 5,000,000\)
= \(N3,000,000\)
Therefore, x = N3,000,000 and y = N5,000,000.
(ii) Interest paid by bank N = 0.32y
= \(0.32 \times N5,000,000\)
= \(N1,600,000\)