Question

Thomas can do a work in 25 days and Mahendra can do it in 20 days. After working together for 5 days, Thomas goes away. In how many days will Mahendra finish the remaining work?

Answer 1

$\large\boxed{ \red{ \underline{ \purple{ \mid} \overline{ \sf \green{Question}} \purple{\mid} }} } : - </p><p> \:$

Thomas can do a work in 25 days and Mahendra can do it in 20 days. After working together for 5 days, Thomas goes away. In how many days will Mahendra finish the remaining work?

$\large\boxed{ \red{ \underline{ \purple{ \mid} \overline{ \sf \red{Answer}} \purple{\mid} }} } : - \: \\ \sf \: Mahendra \: can \: complete \: the \: remaining \\ \sf \: \: work \: in \: 11 \: days \: \\ \\ \large \boxed{ \red{ \underline{ \purple{ \mid} \overline{ \sf \green{Explanation}} \purple{\mid} }} } : -$

Let ,Thomas → T ,Mahendra → M

According to the question -

→ T can do a work in 25 days and M can do that work in 20 days .

→ After doing work together for 5 days,T goes away ,

$\star \sf \: \red{work \: can \: complete} \: by \: T \green{= 25 \: days \: } \\ \\ \implies \sf T \: complete \pink{ \: work \: in \: a \: day }= \frac{1}{25} \\ \\ \bf hence \: \\ \\ \implies \sf \green{ work \: done \: by }\orange{ \: M \: in \: one \: day} = \frac{1}{20} \\ \\ \star \sf \: \red{ together \: they \: can \:} complete \: work \: \\ \sf \: \: \blue{\: in \: a \: day \: \: = } \frac{1}{25} + \frac{1}{20} \: \: \: \: \: \: \: of \: work \: \\ \\ \: \bf \: therefore \\ \\ \to \sf \: \green{ together \: } \:they \: are \: completing \: work \: \\ \: \: \: \: \: \: \sf \red{ in \: 5 \: days \: } = \frac{5}{25} + \frac{5}{20} \: \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf = \frac{1}{5} + \frac{1}{4} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf = \frac{9}{20} \: of \: work \:$

Hence ,

$\implies \sf \red{ \: remaining \: work} \: = 1 - \frac{9}{20} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{11}{20}$

Therefore ,

$\mapsto \sf \red{ \: M \: can \: complete \:} the \: \green{remaining \: work \: } \\ \\ \mapsto \sf \: \frac{ \frac{11}{20} }{ \frac{1}{20} } = 11 \: days \:$

Hence , Mahendra can complete the remaining the work in 11 days

Answer 2

Step-by-step explanation:

Question:

Thomas can do a work in 25 days and Mahendra can do it in 20 days. After working together for 5 days, Thomas goes away. In how many days will Mahendra finish the remaining work?

Answer:

Let Thomas be x and Mahendra be y

Work can complete by x = 25 days

x complete it in a day = 1/25 of the work.

Work can complete by y = 20 days

y complete the work in a day = 1/20 of the work.

The total work can be completed by both of them = 1/25 + 1/20 = 9/100 of the work

Both of them can complete the work in 5 days = 9/100 × 5 = 45/100 of the work = 9/20 of the work.

Left remaining work = 1- 9/20 = 11/20 of work.

The remaining work can be completed by y = 11/20 ÷ 1/20 = 11 days.

Therefore, Mahendra can complete the remaining work in 11 days.