Question

Michael finished colouring a picture in 7/12 hour. Vaibhav finished colouring the same picture in 3/4hour. Who worked longer? By what fraction was it longer​

Answer 1

Here,

$\tiny \text{Time taken by Micheal to finish colouring the picture = }{ \frac{7}{12} }$

$\tiny{ \text{Time taken by Vaibhav to finish colouring the picture = }{ \frac{3}{4} }}$

■ To find :

1. Who (either Micheal or Vaibhav) worked longer ?
2. By what fraction did their working time differ ?

$\overline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }$

☆ SOLUTION :-

• Making denominator of each fraction equal, So

$\boxed{ \: \: \: \: \: \: \: \: \: \: \sf \frac{7}{12} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \frac{3}{4} \: \: \: \: \: \: \: \: \: \: \: }\\ \\ = > \tt \frac{7 \times1 }{12 \times 1} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \frac{3 \times 3}{4 \times 3} \\ \\ = > \overline{\underline{\tt \: \: \: \frac{7}{12} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \frac{9}{12} \: \: \: \: \: }}$

• Now, The fraction whose numerator is larger will be greater among given fractions.

$\huge \mapsto \: \: \: \: \: \bf \frac{9}{12} > \frac{7}{12} \\ \\ \large \: \longrightarrow \: \: \frac{3}{4} > \frac{7}{12} \\ \\ \boxed{ \: \boxed{\small \:\therefore \text { \: \: Vaibhav's time} \red> \text{Micheal's time} \: } \: }$

Thus,

• Finding the difference of two fractions (here)

$= > \frac{3}{4} - \frac{7}{12} \\ \\ = > \frac{9 - 7}{12} \: \: = \frac{2}{12} \: \: \: = \tt \red{\frac{1}{6} }$

$\overline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }$

Hence,

• Vaibhav had worked for longer period of time.
• Also, Vaibhav had worked 1/6 hours more than Micheal.