A takes three times as much time as B or twice as much time as C to finish a piece of work. Working together, they can finish the work in 3 days. B can do the work alone in how many days?
A
14 days
B
8 days
C
6 days
D
10 days
উত্তরের বিবরণ
Question: A takes three times as much time as B or twice as much time as C to finish a piece of work. Working together, they can finish the work in 3 days. B can do the work alone in how many days?
Solution:
ধরা যাক,
A, B ও C যথাক্রমে কাজটি শেষ করতে সময় লাগে x, x/3, এবং x/2 দিন।
তারা একসাথে ৩ দিনে কাজ শেষ করে।
অর্থাৎ তাদের একদিনের কাজ হলো 1/3।
∴ A + B + C এর একদিনের কাজ = (1/x) + (3/x) + (2/x)
= (1 + 3 + 2)/x
= 6/x
এখন,
6/x = 1/3
∴ x = 18
∴ B একা কাজ শেষ করতে সময় নেবে = 18/3 = 6 দিন।
0
Updated: 1 week ago
A can complete a piece of work in 6 days working 8 hours a day, and B can complete the same work in 12 days working 8 hours a day. How long will it take them to complete the work together if they work 4 hours a day?
Created: 2 weeks ago
A
6 days
B
5 days
C
10 days
D
8 days
Question: A can complete a piece of work in 6 days working 8 hours a day, and B can complete the same work in 12 days working 8 hours a day. How long will it take them to complete the work together if they work 4 hours a day?
Solution:
A can complete the work in 8 × 6 = 48 hours
1 hour's work of A = 1/48 part
B can complete the work in 8 × 12 = 96 hours
1 hour's work of B = 1/96 part
(A + B)'s 1 hour's work = (1/48) + (1/96) part
= (2 + 1)/96 part
= 3/96 part
= 1/32
∴ Time taken by (A + B) working 4 hours daily = 32/(1 × 4)
= 8 days
0
Updated: 2 weeks ago
If A and B can complete a work together in 10 days, B and C together in 15 days, and A and C together in 12 days, then in how many days can B alone complete the work?
Created: 1 week ago
A
24 days
B
48 days
C
54 days
D
36 days
Question: If A and B can complete a work together in 10 days, B and C together in 15 days, and A and C together in 12 days, then in how many days can B alone complete the work?
Solution:
মনে করি,
সম্পূর্ণ কাজ = 1 অংশ
∴ (A + B) একদিনে করে = 1/10 অংশ। ..........(1)
(B + C) একদিনে করে = 1/15 অংশ। ..........(2)
(A + C) একদিনে করে = 1/12 অংশ। ..........(3)
(1), (2), (3) যোগ করে পাই,
2 × (A + B + C) = (1/10) + (1/15) + (1/12)
⇒ 2 × (A + B + C) = (6 + 4 + 5)/60 = 15/60
⇒ 2 × (A + B + C) = 1/4
⇒ (A + B + C) = 1/8
∴ A, B এবং C একসাথে একদিনে করে = 1/8 অংশ।
(A + B + C) একসাথে একদিনে করে 1/8 অংশ।
(A + C) একসাথে একদিনে করে 1/12 অংশ।
∴ B-এর একদিনের কাজ = 1/8 - 1/12
= (3 - 2)/24
= 1/24
অর্থাৎ,
B সম্পূর্ণ কাজ করে = (1 ÷ 1/24) = 24 দিনে
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
