Question

Ashwin distributes 30 sweets between Shweta and Pallavi in the ratio 2:3. How many and what percentage of sweets do Shweta and Pallavi get?

Answer 1

Hint:
In mathematics, a ratio is used for comparing two or more quantities that are measured in the same units. A ratio is a general term independent of a unit. For ratios written as a:b, the first term i.e. ‘a’ is known as the antecedent and the second term i.e. ‘b’ is known as the consequent.
If two ratios have the same value when simplified, then they are equivalent ratios.
Percentage is a number or ratio is expressed as a fraction of 100. The percentage formula is given as -
${\text{Percentage = }}\left( {\dfrac{{{\text{Value}}}}{{{\text{Total value}}}}} \right){\text{ \times 100}}$
So here, Take $x$ as the ratio coefficient.
Total number of sweets $ = 30$ and ratio is $2:3$
Let the number of sweets to Shweta be $2x$ and to Pallavi be $3x$ .Hence, the total number of sweets is $5x$ .
Find x, then find the number of sweets received by both.
${\text{Percentage of sweets received by a person = }}$ $\dfrac{{{\text{Sweets received by a person}}}}{{{\text{Total number of sweets}}}} \times 100$

Complete step by step solution:
Total sweets $ = 30$
Ratio of the sweets received by Shweta and Pallavi is $2:3$
Let $x$ be ratio coefficient.
∴ Sweets received by Shweta = $2x$
And sweets received by Pallavi = $3x$
${\text{Total sweets = 2x + 3x = 5x}}$
But given
$5x = 30$
$\therefore x = \dfrac{{30}}{5} = 6$
$\therefore {\text{Sweets received by Shweta = 2}} \times {\text{6}}$
$ = 12$
${\text{and by Pallavi = 3}} \times {\text{6}}$
$ = 18$
$\therefore {\text{Percentage of sweets received by Shweta = }}\dfrac{{12}}{{30}} \times 100$
$ = 40\% $
${\text{and percentage of sweets received by Pallavi = }}\dfrac{{18}}{{30}} \times 100$
$ = 60\% $

Note:
The order of the terms in ratios is very important i.e. the positions of antecedent and consequent are not interchangeable.
Fraction can be converted to percentage simply by multiplying the given fraction by 100 and to convert a percent into a fraction, divide the number by 100.
To increase a number by x% percentage, multiply the number by $\left[ {\dfrac{{100 + x}}{{100}}} \right]$
To decrease a number by x% percentage, multiply the number by $\left[ {\dfrac{{100 - x}}{{100}}} \right]$
To find the percent increment, we use ${\text{Percent increment = }}\left[ {\dfrac{{{\text{Final value - Initial value}}}}{{{\text{Initial value}}}} \times 100} \right]$