Question

In an examination Sneha got 30% marks more then Kumar, Kumar got 5% less than Reema and Reema got 20% more than Suresh.If Suresh got 400 marks out of 600 the marks obtained by Shneha is?

Answer 1

Given:-

• Sneha got 30% more marks than Kumar.
• Kumar got 5% less marks than Reema.
• Reema got 20% more marks than Suresh.
• Suresh got 400 marks out of 600 marks.

To find

Marks of Sneha

Solution

First we will find the marks of Reema

Since, Reema got 20% more marks than Suresh, therefore we can conclude

Reema's Marks = Suresh's Marks + 20% of Suresh's Marks

$\sf \implies Marks \: of \: Reema = \dfrac{400}{600} + 20 \% \; of \ \dfrac{400}{600}$

$\sf \implies Marks \: of \: Reema = \dfrac{400}{600} + \dfrac{20}{100} \times \dfrac{400}{600}$

Here, we can reduce the fractions into their lowest terms as reducing it to lowest terms won't change the value of marks. We can later convert them into their original marks.

$\sf \implies \dfrac{2}{3} + \dfrac{1}{5} \times \dfrac{2}{3}$

$\sf \implies \dfrac{2}{3} + \dfrac{2}{15}$

$\sf \implies \dfrac{10+2}{15}$

$\sf \implies \dfrac{12}{15}$

$\sf \implies \dfrac{4}{5}$

$\bf Marks \: of \: Reema = \dfrac{4}{5} \: or \: \dfrac{480}{600}$

___________________________

Now we will find the marks or Kumar.

Since, Kumar got 5% less marks than Reema, therefore we can conclude,

Kumar's marks = Reema's marks - 5% of Reema's marks.

$\sf \implies Kumar's \ Marks = \dfrac{4}{5}-5\% \ of \ \dfrac{4}{5}$

$\sf \implies \dfrac{4}{5}- \dfrac{5}{100} \times \dfrac{4}{5}$

$\sf \implies \dfrac{4}{5}- \dfrac{1}{20} \times \dfrac{4}{5}$

$\sf \implies \dfrac{4}{5}- \dfrac{1}{25}$

$\sf \implies \dfrac{20-1}{25}$

$\sf \implies \dfrac{19}{25}$

$\bf Marks \ of \ Kumar = \dfrac{19}{25} \: or \ \dfrac{456}{600}$

_____________________________

Finally, we will find marks obtained by Sneha.

Since, Sneha got 30 % more marks than Kumar, therefore we can conclude

Sneha's marks = Kumar's Marks + 30% of Kumar's Marks.

$\sf \implies Sneha's \ Marks= \dfrac{19}{25} + 30\% \ of \ \dfrac{19}{25}$

$\sf \implies \dfrac{19}{25} + \dfrac{30}{100}\times\dfrac{19}{25}$

$\sf \implies \dfrac{19}{25} + \dfrac{3}{10}\times\dfrac{19}{25}$

$\sf \implies \dfrac{19}{25} + \dfrac{57}{250}$

$\sf \implies \dfrac{190+57}{250}$

$\sf \implies \dfrac{247}{250}$

$\bf \therefore Marks \: of \: Sneha \: are \quad \dfrac{247}{250} \ or \ \dfrac{592.8}{600}$

Sneha got 592.8 marks out of 600

Hope it helps