P and Q can do a job in 3 days. Q and R can do the same job in 4 days, while R and P can do it in 12 days. In how many days the job will be finished when P, Q and R working together.
A
10 days
B
3 days
C
4 days
D
12 days
উত্তরের বিবরণ
Question: P and Q can do a job in 3 days. Q and R can do the same job in 4 days, while R and P can do it in 12 days. In how many days the job will be finished when P, Q and R working together.
Solution:
Given that,
(P + Q)'s 1 day's work = 1/3
(Q + R )'s 1 day's work= 1/4
and
(R + P)'s 1 day's work = 1/12
Now, (P + Q) + (Q + R) + (R + P) = 2(P + Q + R)'s 1 day's work = (1/3) + (1/4) + (1/12)
= (4 + 3 + 1)/12
= 8/12 = 2/3
∴ (P + Q + R)'s 1 day's work = 2/(3 × 2) = 1/3
So, P + Q + R can complete the job in = 3 days
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Updated: 2 weeks ago
If Rafi and Suman together can complete a job in 12 days. If Rafi alone can finish the job in 20 days, in how many days can Suman alone complete the work?
Created: 2 weeks ago
A
25 days
B
60 days
C
45 days
D
30 days
Question: If Rafi and Suman together can complete a job in 12 days. If Rafi alone can finish the job in 20 days, in how many days can Suman alone complete the work?
Solution:
Rafi and Suman together can complete a piece of work in 12 days
Rafi and Suman together can complete in 1 day = 1/12
Rafi alone in 20 days
Rafi alone in one day = 1/20
∴ Suman complete in one day = (1/12) - (1/20)
= (5 - 3)/60
= 2/60
= 1/30
∴ Suman can complete the work in 30 days
0
Updated: 2 weeks ago
Rafi and Shafi can paint a room in 4 days. Shafi can do it alone in 6 days. How many days will Rafi take to paint the room alone?
Created: 1 week ago
A
12 days
B
10 days
C
15 days
D
9 days
Question: Rafi and Shafi can paint a room in 4 days. Shafi can do it alone in 6 days. How many days will Rafi take to paint the room alone?
Solution:
ধরা যাক,
Rafi একা কাজটি করতে x দিন সময় নেন।
∴ Rafi-র 1 দিনের কাজ = 1/x
∴ Shafi-র 1 দিনের কাজ = 1/6 (কারণ সে একা ৬ দিনে কাজটি করে)
তারা দুজনে মিলে ৪ দিনে কাজ শেষ করে।
∴ তাদের 1 দিনের একত্রে কাজ = 1/4
এখন,
(1/x) + (1/6) = 1/4
⇒ (6 + x) / (6x) = 1/4
⇒ 4(6 + x) = 6x
⇒ 24 + 4x = 6x
⇒ 24 = 6x - 4x = 2x
⇒ x = 24 / 2 = 12
∴ Rafi একা কাজটি করতে 12 দিন সময় নেবে।
0
Updated: 1 week ago
Three workers can do a job in 6 days. Two of the workers work twice as fast as the third. How long would it take one of the faster workers to do the job himself?
Created: 2 weeks ago
A
15 days
B
18 days
C
24 days
D
12 days
Question: Three workers can do a job in 6 days. Two of the workers work twice as fast as the third. How long would it take one of the faster workers to do the job himself?
Solution:
Let,
the first and 2nd worker need x days.
Third worker needs 2x days
ATQ,
(1/x) + (1/x) + (1/2x) = 1/6
⇒ (2 + 2 + 1)/2x = 1/6
⇒ 5/2x = 1/6
⇒ 2x = 30
∴ x = 15
So the one faster worker alone will take 15 days to complete the job.
0
Updated: 2 weeks ago
