Question

1- the salary of Gopal was increased by 10% and then the increased salary was decreased by 10% . find the net increasing or decreasing percent in his original salary.

2- After deducting 4% of a bill, the amount still to be paid is ₹ 1488. how much was the original bill ?

3- the weight of a boy was 40 kg. but 8t was wrongly measured. as 42kg. find the error percent.

Answer 1

1 answer is 0 percent

Answer 2

Answer:

The net decreasing percent in original salary of gopal is 1% .

The original bill is ₹ 1550 .

The percentage error is 5% .

Step-by-step explanation:

Answer:

Step-by-step explanation:

First part  

As given  

The salary of Gopal was increased by 10% and then the increased salary was decreased by 10% .

Let us assume that the original salary be s .

10% is written in the decimal form  

$= \frac{10}{100}$

= 0.10  

Salary increase by 10% = 0.10 × Salary amount  

= 0.10s

Thus  

Salary becomes after increase of 10% = Salary +Salary increase by 10%

= s + 0.10s  

= 1.10s

Thus  

Initial change salary =1.10s

As the salary is decreased by 10% .

Salary decrease by 10% = 0.10 × Salary becomes after increase of 10%  

= 0.10 × 1.10s

= 0.11s

Thus  

Salary becomes after 10% decreases = Salary becomes after increase of 10% - Salary decrease by 10%

= 1.10s - 0.11s

= 0.99s  

Thus  

Final change in salary = 0.99s  

$Net\ increases\ or\ decreases = \frac{(Original\ salary- Final\ change\ in\ salary)\times 100}{Original\ Salary}$

Put all the values in the formula  

$Net\ increases\ or\ decreases\ percentage = \frac{(s- 0.99s)\times 100}{s}$

$Net\ increases\ or\ decreases\ percentage = \frac{-0.01s\times 100}{s}$

$Net\ increases\ or\ decreases\ percentage = \frac{-100s}{100s}$

= -1%  

(As the negative sign in the above expression represented the net decreases.)

Thus the net decreasing percent in original salary of gopal is 1% .

Second part  

Let us assume that the original bill is y.

After deducting 4% of a bill.

The amount still to be paid is ₹ 1488.

4% is written in the decimal form  

$= \frac{4}{100}$

= 0.04  

Deducted amount = 0.04 × Original bill

                              = 0.04y

Thus

Original bill - Deducted amount = Amount still to be paid

Put all the values in the above

y - 0.04y = 1488

0.96y = 1488

$y = \frac{1488}{0.96}$

y = ₹ 1550

Therefore the original bill is ₹ 1550 .

Third part

Formula

$Percentage\ error = \frac{Change\ in\ value\times 100}{Actual\ value}$

Where

Change in value = |Approx value - Actual value|

The weight of a boy was 40 kg. but 8t was wrongly measured. as 42kg.

Actual value = 40 kg

Approx value = 42 kg

Put all the values in the above

Change in value = |42 - 40|

                           = 2 kg

Put all the values in the percentage error formula

$Percentage\ error = \frac{2\times 100}{40}$

$Percentage\ error = \frac{200}{40}$

Percentage error = 5%

Therefore the percentage error is 5% .