The problem has two parts: (a) Evaluate the expression $(3.69 \times 10^5) \div (1.64 \times 10^{-3})$ and leave the answer in standard form. (b) A man invested N20,000 in bank A at $y\%$ simple interest per annum and N25,000 in bank B at $1.5y\%$ simple interest per annum. His total interest at the end of the year was N4,600. Find the value of $y$.

AlgebraScientific NotationArithmetic OperationsSimple InterestPercentage
2025/4/21

1. Problem Description

The problem has two parts:
(a) Evaluate the expression (3.69×105)÷(1.64×103)(3.69 \times 10^5) \div (1.64 \times 10^{-3}) and leave the answer in standard form.
(b) A man invested N20,000 in bank A at y%y\% simple interest per annum and N25,000 in bank B at 1.5y%1.5y\% simple interest per annum. His total interest at the end of the year was N4,
6
0

0. Find the value of $y$.

2. Solution Steps

(a) We are asked to evaluate (3.69×105)÷(1.64×103)(3.69 \times 10^5) \div (1.64 \times 10^{-3}) and leave the answer in standard form.
We can rewrite the expression as:
3.69×1051.64×103=3.691.64×105103\frac{3.69 \times 10^5}{1.64 \times 10^{-3}} = \frac{3.69}{1.64} \times \frac{10^5}{10^{-3}}
We can simplify the expression by dividing 3.693.69 by 1.641.64:
3.691.642.25\frac{3.69}{1.64} \approx 2.25
We can simplify the expression by dividing 10510^5 by 10310^{-3}:
105103=105(3)=105+3=108\frac{10^5}{10^{-3}} = 10^{5 - (-3)} = 10^{5+3} = 10^8
Therefore, we have:
2.25×1082.25 \times 10^8
(b) The simple interest formula is:
Interest=Principal×Rate×TimeInterest = Principal \times Rate \times Time
The interest from bank A is:
IA=20000×y100×1=200yI_A = 20000 \times \frac{y}{100} \times 1 = 200y
The interest from bank B is:
IB=25000×1.5y100×1=250×1.5y=375yI_B = 25000 \times \frac{1.5y}{100} \times 1 = 250 \times 1.5y = 375y
The total interest is:
IA+IB=200y+375y=575yI_A + I_B = 200y + 375y = 575y
We are given that the total interest is N4,600:
575y=4600575y = 4600
Dividing both sides by 575, we get:
y=4600575=8y = \frac{4600}{575} = 8

3. Final Answer

(a) 2.25×1082.25 \times 10^8
(b) y=8y = 8

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