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

Answer: (b)

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

Answer: (b)

Decimal equivalent of :

$3/4$ = 0.75 and $5/6$ = 0.833

Now, $2/3$ = 0.66, $1/2$ = 0.5 ,

$4/5$ = 0.8 and $9/10$ = 0.9

Clearly, $4/5$ lies between $3/4$ and $5/6$.

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: (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

Answer: (c)

Let the original fraction be $x/{x + 3}$.

${x + 7}/{x + 3 - 2} = 2$

$x + 7 = 2x + 2$

$x = 7 - 2 = 5$

Required sum =$x + x + 3 = 2x + 3 = 10 + 3 = 13$

Answer: (c)

$0.4\ov{23} = {423- 4}/990 = 419/990$