model 3 fraction of numbers Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (d)

Let the total number of students in a class be x

According to question,

Number of girls = $3/5$ x

and number of boys = x – $\text"3x"/5$ = $2/5$ x

Number of girls who are absent

=$3/5 × 2/9$x = $\text"6x"/45$

and number of boys who are absent

=$2/5 × 1/4$ × x = $\text"x"/10$

Total number of students who are present

= x - $\text"6x"/45 - \text"x"/10$

= $\text"(90 – 12 -9)x"/90$

= $\text"69x"/90 = \text"23x"/90$

Therefore, the $23/30$ part of the students are present in the class.

Answer: (a)

$1/2$ of 1% = $1/2 × 1/100 = {0.01}/2$ = 0.005

Answer: (c)

Let the fraction = x

According to the question;

$6/7$ of x = $x/{6/7} - 13/70$

= $\text"6x"/7 = \text"7x"/6 - 13/70$

= $\text"7x"/6 - \text"6x"/7 = 13/70$

= $\text"49x - 36x"/42 = 13/70$

= $\text"13x"/42 = 13/70$

x = ${13×42}/{70×13} = 3/5$

Answer: (b)

1.$\ov{27}$ =1$27/99 = 1{3}/11 = 14/11$

Answer: (d)

$2/3 × 3/4 = 1/2$

Answer: (b)

Let numerator be $x$, then denominator = 11 – $x$.

Fraction =$x/{11 - x}$

Again, ${x + 2}/{11 – x + 2} = x/{11 - x} + 1/24$

⇒ ${x + 2}/{13 - x} – x/{11 - x} = 1/24$

⇒ ${11x – x^2 + 22 – 2x – 13x +x^2}/{(13 - x)(11 - x)} = 1/24$

⇒ ${22 – 4x}/{(13 - x)(11 - x)} = 1/24$

⇒ $528 – 96x = 143 – 24x + x^2$

⇒ $x^2 + 72x – 385$ = 0

⇒ $x^2 + 77x – 5x – 385$ = 0

⇒ $x (x + 77) - 5 (x + 77)$ = 0

⇒ (x - 5) (x + 77) = 0 ⇒ x = 5

Denominator = 11 - 5 = 6

Difference = 6 - 5 = 1