Question

Which of the following will have the maximum change in their values if 5 is added to both the numerator and denominator of all the fractions?
(1)3/4
(2)2/3
(3)4/7
(4)5/7​

Answer 1

$\dfrac{2}{3}$ and $\dfrac{4}{7}$ will have the maximum change in their values if 5 is added to both the numerator and denominator of all the fractions.

Step-by-step explanation:

(1) $\dfrac{3}{4}$

When 5 is added to both the numerator and the denominator, new fraction is

$\dfrac{3+5}{4+5}=\dfrac{8}{9}$

So required change is

$\dfrac{new\:fraction-old\:fraction}{old\:fraction}\times 100\%$

$=\dfrac{\frac{8}{9}-\frac{3}{4}}{\frac{3}{4}}\times 100\%$

= 18.52% (approximately)

(2) $\dfrac{2}{3}$

When 5 is added to both the numerator and the denominator, new fraction is

$\dfrac{2+5}{3+5}=\dfrac{7}{8}$

So required change is

$\dfrac{new\:fraction-old\:fraction}{old\:fraction}\times 100\%$

$=\dfrac{\frac{7}{8}-\frac{2}{3}}{\frac{2}{3}}\times 100\%$

= 31.25%

(3) $\dfrac{4}{7}$

When 5 is added to both the numerator and the denominator, new fraction is

$\dfrac{4+5}{7+5}=\dfrac{9}{12}$

So required change is

$\dfrac{new\:fraction-old\:fraction}{old\:fraction}\times 100\%$

$=\dfrac{\frac{9}{12}-\frac{4}{7}}{\frac{4}{7}}\times 100\%$

= 31.25%

(4) $\dfrac{5}{7}$

When 5 is added to both the numerator and the denominator, new fraction is

$\dfrac{5+5}{7+5}=\dfrac{10}{12}$

So required change is

$\dfrac{new\:fraction-old\:fraction}{old\:fraction}\times 100\%$

$=\dfrac{\frac{10}{12}-\frac{5}{7}}{\frac{5}{7}}\times 100\%$

= 16.67% (approximately)

So, $\dfrac{2}{3}$ and $\dfrac{4}{7}$ will have the maximum change in their values.

#SPJ3

Answer 2

Answer:

Concept:

Number system from quantitative aptitude.

Explanation:

Given:

(1) 3/4

(2) 2/3

(3) 4/7

(4) 5/7​

Find:

Which of the given fractions will have the maximum change in their values if 5 is added to both the numerator and denominator.

Solution:

(1)

$\begin{aligned}&\ 2 / 3=0.667 \\\\&\ (2+5) /(3+5)=7 / 8=0.875 \\\\&\text { Change }=0.875-0.667 \ =0.208\end{aligned}$

(2)

$\begin{aligned}&\ 3 / 4=0.75\\\\&\ (3+5) /(4+5)=8 / 9=0.89 \\\\&\text { Change }=0.89-0.75 \ =0.14\end{aligned}$

(3)

$\begin{aligned}&\ 4 / 7=0.57 \\\\&\ (4+5) /(7+5)=9 / 12=0.75 \\\\&\text { Change }=0.75-0.57 \ =0.18\end{aligned}$

(4)

$\begin{aligned}&\ 5 / 7=0.71 \\\\&\ (5+5) /(7+5)=10 / 12=0.83 \\\\&\text { Change }=0.83-0.71 \ =0.12\end{aligned}$

The maximum change occurred for 2/3

#SPJ2