Given below are two statements:

Statement (I): A man sells his goods at 10% profit. If he sells his goods at 15% profit, he gets 160rupes more. The cost price of his goods is 4.200rupes

Statement(II): A man spends 80% of his earnings. His earnings increased by 25% and his expenses. increased by 20%. The man's savings thus increased by 45%.

In the light of the above statements, choose the correct answer from the options given below:

The correct answer is Statement (I) is false, but statement (II) is true.

Let us analyze both statements step-by-step to understand why this option is correct.

Step-by-step Analysis of Statement (I):

Let the cost price of the goods be $CP$.

Initially, the man sells his goods at a 10% profit. The selling price ($S{P}_1$) is given by:
$S{P}_1=CP+0.10CP=1.10CP$

If he sells them at a 15% profit, the new selling price ($S{P}_2$) becomes:
$S{P}_2=CP+0.15CP=1.15CP$

According to the statement, selling at a 15% profit instead of a 10% profit yields 160 rupees more. Therefore, we can set up the equation:
$S{P}_2-S{P}_1=160$

Substitute the values in terms of $CP$:
$1.15CP-1.10CP=160$
$0.05CP=160$

Solving for $CP$:
$CP=\frac{160}{0.05}=3200\text{rupees}$

Since the actual cost price is 3,200 rupees, but Statement (I) claims the cost price is 4,200 rupees, Statement (I) is false.

Step-by-step Analysis of Statement (II):

Let the man's initial earnings (Income) be 100 units.
Since he spends 80% of his earnings, his initial expenses (Expenditure) are 80 units.
His initial savings are calculated as:
$\text{Savings}=\text{Income}-\text{Expenditure}=100-80=20\text{units}$

Now, his earnings increase by 25%:
$\text{New Income}=100\times 1.25=125\text{units}$

His expenses increase by 20%:
$\text{New Expenditure}=80\times 1.20=96\text{units}$

His new savings are:
$\text{New Savings}=125-96=29\text{units}$

Now, we find the percentage increase in his savings:
$\text{Increase in savings}=\text{New Savings}-\text{Initial Savings}=29-20=9\text{units}$

Percentage increase in savings is:
$\text{Percentage Increase}=\left(\frac{9}{20}\right)\times 100=45\%$

Since the percentage increase matches the 45% stated in the problem, Statement (II) is true.

Thus, Statement (I) is false and Statement (II) is true.