Question

5.) In a school the ratio of boys and girls are in the ration 5:6. 25% of boys will get scholar ship and 20% of girls will get scholar ship what % of students won't get scholarship? *​

Answer 1

$\sf\pink {\underline{\underline{\purple{Given :}}}}$

• In the given question the ratio of the boys and girls is 5 : 6.
• Where, 25% boys will be getting the scholarship.
• And, 20% of girls will be getting the scholarship.

$\sf\pink {\underline{\underline{\purple{To \: find :}}}}$

• The % of students will not get the scholarship.

$\sf\pink {\underline{\underline{\purple{Solution :}}}}$

• Here, it is that the ratio of boys and girls is 5 : 6

Lets assume that the no. of boys and girls are :

➠ 5x and 6x respectively.

Then, Total no. of students will be :

➠ 5x + 6x = 11x

Now,

${ \underline{ \underline{ \green{ \bf Calculation \: for \: boys : }}}}$

Where,

➠ No. of boys are = 5x

➠ % of boys getting Scholarship = 25%

Hence,

∵ if 25% of boys are getting Scholarship

$\sf \therefore$ % of boys won't be getting the scholarship is = (100 - 25)% = 75%.

75% of 5x won't get scholarship,

➠ 75/100 × 5x

➠ ¾ × 5x

➠ 15x/4 .

Thereafter,

${ \underline{ \underline{ \green{ \bf Calculation \: for \: girls : }}}}$

Where,

➠ No. of girls are = 6x

➠ % of girls getting Scholarship = 20%

Hence,

∵ if 20% of girls are getting Scholarship

$\sf \therefore$ % of girls won't be getting the scholarship is = (100 - 20)% = 80%.

80% of 6x won't be getting the scholarship :

➠ 80/100 × 6x

➠ ⅘ × 6x

➠ 24x/5.

Therefore,

Total no. of students won't be getting the scholarship is :

$<strong> </strong> \sf \to \: \frac{15x}{4} + \frac{24x}{5}$

$\sf \to \: \frac{75x + 96x}{20}$

${\blue{ \bf \to \frac{171x}{20} }}$

% of students won't be getting the scholarship :

Using the formula :

$\red{ \underline{ \boxed{ \sf{ \frac{Total \: no. \: students \: didnt \:got \: scholarship }{Total \: no. \: students \: } \times 100}}}}$

$\dashrightarrow \sf \frac{ \frac{171x}{20} }{11x} \times 100$

$\dashrightarrow \sf \: \frac{{171 \cancel x}}{ {11 \cancel x} \times \cancel{20}} \times \cancel{100}$

$\dashrightarrow \sf \frac{171 \times 5}{11}$

$\dashrightarrow \sf \frac{855}{11}$

$\dashrightarrow \sf 77.72$

${\orange {\sf \therefore Required \: answer : }}\\ \sf \blue{\underline{\boxed{\sf{ \dashrightarrow 77.72(approx.)}}}}$

Answer 2

${\huge{\pink{\underline{\underline{QuEsTiOn}}}}}$
In a school the ratio of boys and girls are in the ration 5:6. 25% of boys will get scholar ship and 20% of girls will get scholar ship what % of students won't get scholarship?

${\huge{\pink{\underline{\underline{SoLuTiOn}}}}}$
Let the no. of boys be 5x
and no. of girls be 6x
So,total no. of students is 5x+6x=11x

So,the no. of boys got scholarship =$25% of boys\\=25% of 5x\\=\frac{25}{100} \times 5x\\= \frac{1}{4} \times 5x\\= \frac{5x}{4}$

No. of girls got scholarship=$20% of girls\\=20%of 6x\\=\frac{20}{100} \times 6x\\= \frac{1}{5} \times 6x \\= \frac{6x}{5}$

Total no. of student got scholarship=$\frac{5x}{4} + \frac{6x}{5} \\=\frac{25x}{20} + \frac{24x}{20}\\= \frac{25x + 24x}{20}\\= \frac{49x}{20}$

So,no of students won't got scholarship =$11x - \frac{49x}{20}\\ =\frac{220x - 49x}{20}$

%of student won't get scholarship =$\frac{no.\ of\ student| won't\ get}{total\ no.\ of\ student}×100$

$= \frac{ \frac{171x}{20} }{11} \times 100$

$= \frac{ 171x }{11x \times 20} \times 100$

$= \frac{ 171x }{11x } \times 5$

$= \frac{855}{11}$

$=77.87%(approx.)$