Question

Kiran alone can do a piece of work in 15 days and aman can do the same work in 10 days if they start working together in how many days the work be completed​

Answer 1

Answer:

6 days

Step-by-step explanation:

kiran = 15 days

Aman = 10 days

now take LCM = 30

so total work is 30 unit out of which Kiran can do 2 units of work per day while aman can do 3 unit work per day

it means they can do 5 unit work per day

time taken = total work/ efficiency

30/5 = 6 days

another formula is

X×Y/x+y

15×10/15+10

150/25=

6 days

Answer 2

✯Answer✯

❋Given

• Time taken by kiran for the work=15 days
• Time taken by Aman for the work= 10 days

❋To find

• Time taken by both together to complete the work.

❋Solution

$\large{ \sf{ \rightarrow \: kiran \: one \: day \: work = \frac{1}{15} }} \\ \\ \large{ \sf{ \rightarrow \:aman \: one \: day\: work \: = \frac{1}{10} }} \\ \\ \large{ \sf{ \rightarrow \: (kiran + aman) \: one \: day \: work = \frac{1}{15} + \frac{1}{10} }} \\ \\ \large{ \sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{2 + 3}{30} }} \\ \\ \large{ \sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \cancel{ \frac{5}{30}} }}\\ \\ \large{ \sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{6} }} \\ \\ \large{ \sf{ \rightarrow \: time \: taken \: by \: both \: to \: complete \: the \: work = \boxed{ \purple{ 6 \: days}}}}$

✯So Final Answer✯

${ \huge{ \boxed{ \bf{ \green{6 \: days}}}}}$

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✯Related Concept✯

$\large{ \sf{ \underline{ \red{ time \: and \: work}}}}$

❋ If A can do a piece of work in n days, then at a uniform rate of working A will finish 1/n th of work in 1 day.

❋If A can do n times faster than B, Then ratio of work done by A and B is n:1 and ratio of time taken by A and B is 1:n.

❋If A and B can do a work in X days and Y days respectively, then Time taken by both working together= XY/X+Y.

❋If a men and b women can do a picture of work in n days, then c men and d women can do the work in ( nab/bc+ad ) days.