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Let
𝑅
R be the rate at which Ram works (in terms of fraction of job per day).
Let
𝑆
S be the rate at which Shyam works (in terms of fraction of job per day).
From the problem statement:
Ram and Shyam together can finish the job in 8 days.
Ram alone can finish the job in 12 days.
First, find Ram’s rate
𝑅
R:
𝑅
=
1
12
R=
12
1
Next, since Ram and Shyam together can finish the job in 8 days, we have:
(
𝑅
+
𝑆
)
×
8
=
1
(R+S)×8=1
Substitute
𝑅
=
1
12
R=
12
1
into the equation:
(
1
12
+
𝑆
)
×
8
=
1
(
12
1
+S)×8=1
Simplify and solve for
𝑆
S:
Shyam’s 1 day’s work
= 1/8 – 1/12
= (3 – 2)/24
= 1/24
Therefore, Shyam alone will do the work in 24 days.
Answer: Shyam alone will do the work in 24 days.