Question

(Marks:2)
6) If (5/8) of a piece of work is completed in (8/5) days, in how many days can rest of the work be completed?
O (5/8)
O (8/5)
O (24/25)
O (25/24)
​

Answer 1

Given:

• (5/8) of a piece of work is completed in (8/5) days

To Find:

• how many days can rest of the work be completed?

Solution:

• Let's assume that the total part of work to be done is 1

Now,

• the work completed = 5/8 th part

The work left to be done =

• 1/1 - 5/8
• 8/8 - 5/8
• 3/5

Hence,

• 3/5 th part of the work is yet to be done,

Now,

• The time taken to complete 5/8 of work = 8/5 days

So,

• The time taken to complete 1/8th of the work will be

➱ 1/8 = 8/5 × 1/5

➱ 1/8 = 8/25 days

hence,

• 1/8th part oc the work will be done in 8/25 days

Now,

• We have to find the time taken complete 3/8 th part

➱ 8/25 × 3/1

➱ 24/25 days

Hence,

• Option c 24/25 is correct ✅

Thx for the question ♡!!

Answer 2

Given:

• (5/8) th of a piece of work is completed in (8/5) days respectively

To Find:

• how many days can rest of the work be completed?

Solution:

• The remaining work can be done in 24/25 days

Full Solution:

Here,

• ↠Time Taken to do 5 / 8 th part of the work is 8/5 days

Now,

➼ Let's find the remaining part of the work to be completed respectively!

Considering,

↝The total part of the work to be done as 1

• ➱Let's find the remaining work to be done,

${ : \implies} \rm \: remaining \: work \: to \: be \: done = \frac{1}{1} - \frac{5}{8 } \\ \\ \\ { : \implies} \rm \: remaining \: work \: to \: be \: done = \frac{8}{8} - \frac{5}{8} \\ \\ \\ { : \implies} \rm \: remaining \: work \: to \: be \: done = \frac{3}{8} {}^{\star} \: \: \: \: \: \: \: \:$

• Henceforth 3/8 th part of the work is yet to be completed!

➼ Now,

• ↠ let's find the time taken to complete 1/8th part of the work

➼ We know,

• 5/8 th work will be done in 8/5 days

So,

$\longrightarrow \rm \: \frac{5}{8} th \: work \rm = \frac{8}{5} \: days \\ \\ \\ \longrightarrow \rm \frac{1}{8}th \: work = \frac{8}{5} \div \frac{5}{1} \: \\ \\ \\ \longrightarrow \rm \frac{1}{8} th \: work = \frac{8}{5} \times \frac{1}{5} \: \\ \\ \\ \longrightarrow \rm \frac{1}{8} th \: work = \frac{8}{25} days$

Now,

• We have to find in how many days will they complete 3/8 th part

$\longrightarrow \rm \frac{1}{8} th \: part = \frac{8}{25} days \: \: \: \: \: \: \\ \\ \\ \longrightarrow \rm \frac{3}{8} th \: part = \frac{8 \times 3}{25} days \\ \\ \\ \longrightarrow \rm \frac{3}{8} th \: part = \frac{24}{25} days \: \: \: \: \: \: \:$

Therefore:

• The time taken to complete the work is 24/25 days!!