Rahim and Karim can finish a work together in 6 hours. If Rahim takes 3 times as long as Karim to finish the job alone, how long will Karim take to finish the job alone?
A
9 hours
B
8 hours
C
12 hours
D
15 hours
উত্তরের বিবরণ
Question: Rahim and Karim can finish a work together in 6 hours. If Rahim takes 3 times as long as Karim to finish the job alone, how long will Karim take to finish the job alone?
Solution:
ধরি, করিম একা কাজটি শেষ করতে সময় নেয় = x ঘন্টা
রহিম একা কাজটি শেষ করতে সময় নেয় = 3x ঘন্টা
এখন,
করিমের 1 ঘন্টার কাজের পরিমাণ = 1/x অংশ
রহিমের 1 ঘন্টার কাজের পরিমাণ = 1/(3x) অংশ
তারা একসাথে 1 ঘন্টায় কাজ করতে পারে = (1/x) + 1/(3x)
= (3+1)/(3x)
= 4/(3x) অংশ
একসাথে কাজটি শেষ করতে সময় লাগে = 6 ঘন্টা
অর্থাৎ, 6 ঘন্টায় তারা পুরো 1টি কাজ শেষ করে
তাহলে,
(4/3x) × 6 = 1
⇒ 24/(3x) = 1
⇒ 8/x = 1
⇒ x = 8
∴ করিমের কাজটি একা শেষ করতে 8 ঘন্টা সময় লাগবে।
0
Updated: 1 month ago
P and Q together complete a piece of work in x days. If P alone completes the work in (x + 3) days and Q alone completes the piece of work in (x + 12) days, what is the value of 'x'?
Created: 2 months ago
A
8
B
6
C
12
D
4
Question: P and Q together complete a piece of work in x days. If P alone completes the work in (x + 3) days and Q alone completes the piece of work in (x + 12) days, what is the value of 'x'?
Solution:
P's 1 day's work = 1/(x + 3) part
Q's 1 day's work = 1/(x + 12) part
and (P + Q)'s 1 day's work = 1/x
ATQ,
1/(x + 3) + 1/(x + 12) = 1/x
⇒ (x + 12 + x + 3)/(x + 3)(x + 12) = 1/x
⇒ (2x + 15)/(x2 + 15x + 36) = 1/x
⇒ 2x2 + 15x = x2 + 15x + 36
⇒ 2x2 + 15x - x2 - 15x = 36
⇒ x2 = 36
∴ x = 6
0
Updated: 2 months ago
A ferry can carry 30 trucks or 50 motorcycles at a time. If there are 18 trucks on the ferry, how many motorcycles can be loaded onto it?
Created: 1 month ago
A
20
B
24
C
16
D
30
Question: A ferry can carry 30 trucks or 50 motorcycles at a time. If there are 18 trucks on the ferry, how many motorcycles can be loaded onto it?
Explanation:
Given,
30 trucks = 50 motorcycles
∴ 1 truck = 50/30 = 5/3 motorcycles
∴ 18 trucks = 18 × 5/3 = 30 motorcycles
Maximum motorcycles on ferry = 50
∴ Remaining motorcycles that can be loaded = 50 - 30 = 20
So, the ferry can carry 20 more motorcycles along with the 18 trucks.
0
Updated: 1 month ago
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?
Created: 1 month ago
A
14 days
B
8 days
C
6 days
D
10 days
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 month ago
