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'?
A
8
B
6
C
12
D
4
উত্তরের বিবরণ
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 weeks 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
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
15 workers can build 45 chairs working 6 hours per day. How many extra workers are required to produce 60 chairs working 4 hours per day?
Created: 1 week ago
A
0 workers
B
10 workers
C
12 workers
D
15 workers
Question: 15 workers can build 45 chairs working 6 hours per day. How many extra workers are required to produce 60 chairs working 4 hours per day?
Solution:
6 ঘণ্টা কাজ করে 45টি চেয়ার তৈরি করে 15 জন শ্রমিক
1 ঘণ্টা কাজ করে 1টি চেয়ার তৈরি করে = (15 × 6) /45 জন শ্রমিক
4 ঘণ্টা কাজ করে 60টি চেয়ার তৈরি করে = (15 × 6 × 60)/(45 × 4) জন শ্রমিক
= 30 জন
∴ অতিরিক্ত শ্রমিকের সংখ্যা = 30 - 15 = 15 জন
0
Updated: 1 week ago
