Question

In December 2001, a school had 1030 students. In 2002, the strength rose by 5%. But in 2003, the strength went down by 1%. The strength of the school at the end of 2003 was
A
1030 x {frac(4/100)}
B
1030(1 + {frac(4/100)} )
C
1030(1 + {frac(5/100)} )(1- {frac(1/100)} )
D
1030 + {frac(5/100)} - {frac(1/100)}
please answer my question with explaination ...........i will mark you as brainliest

Answer 1

Given:

We have been given that the total number of students in a school in 2001 was 1030, which increased by 5% in 2002 and then decreased by 1% in 2003.

To find:

We have to find the total number of students(strength) of the school at the end of 2003.

Solution:

Strength at the end of 2001 → 1030 [Given]

Now, we will find total number strength the end of 2002.

For this we will use the formula;

Strength at the end of 2002 = Total Strength in 2001 + Number of students increased due to increment of 5% in 2001.--------------(1)

Number of students increased = 5% of 1030

                                                     $=\frac{5}{100}$ × 1030

Putting the values in (1) we get,

Total number of students at the end of 2002 = 1030 +  $\frac{5}{100}$ × 1030

                                                                             = 1030 × (1 + $\frac{5}{100}$ )

Now, as we have found out the strength of 2002, we will find out the strength at the end of 2003. For this,

Strength at the end of 2003 = Total strength at the end of 2002 - Number of students decreased due 1% reduction in 2002 strength.

So,

Number of students decreased = 1% of 1030 × (1 + $\frac{5}{100}$ )

                                                       = $\frac{1}{100}$ ×  1030 × (1 + $\frac{5}{100}$ )

Now,

Strength at the end of 2003 = 1030 × (1 + $\frac{5}{100}$ ) - $\frac{1}{100}$ ×  1030 × (1 +

Taking 1030 × (1 + $\frac{5}{100}$ ) common from both we get,

                                                = 1030 × (1 + $\frac{5}{100}$ ) (1 - $\frac{1}{100}$ )

So the Strength of the class at the end of 2003 is

1030 × (1 + $\frac{5}{100}$ ) (1 - $\frac{1}{100}$ ), which matches with option C.

So, option C is the correct answer.