Three mechanics A, B, and C can manufacture 120 units in 12, 20, and 30 hours respectively. What is the ratio of the time taken by A alone to complete the work to the time taken by all three working together to complete the same work?
A
5 : 2
B
4 : 3
C
3 : 1
D
2 : 1
উত্তরের বিবরণ
Question: Three mechanics A, B, and C can manufacture 120 units in 12, 20, and 30 hours respectively. What is the ratio of the time taken by A alone to complete the work to the time taken by all three working together to complete the same work?
Solution:
(A + B + C) together can do in 1 hour = (1/12) + (1/20) + (1/30)
= (5 + 3 + 2)/60
= 10/60
= 1/6
So, working together they complete the work in 6 hours.
And A alone takes 12 hours.
∴ Ratio of the time taken by A and (A + B + C) =12 : 6 = 2 : 1
0
Updated: 2 weeks ago
A worker earns Tk. 300 on the first day and spends Tk. 150 on the second day, earns Tk. 300 on the third day and again spends Tk. 150 on the fourth day, and so on. On which day would he have had Tk. 1500?
Created: 1 week ago
A
16th day
B
17th day
C
19th day
D
21st day
Question: A worker earns Tk. 300 on the first day and spends Tk. 150 on the second day, earns Tk. 300 on the third day and again spends Tk. 150 on the fourth day, and so on. On which day would he have had Tk. 1500?
Solution:
1ম দিনে আয় = 300 টাকা
2য় দিনে ব্যয় = 150 টাকা
∴ প্রতি 2 দিনে জমা হয় = 300 - 150 = 150 টাকা
শুধু 1ম দিনে আয় করায় হাতে থাকে = 300 টাকা
অতএব, 1500 - 300 = 1200 টাকা আরও জমা করতে হবে।
150 টাকা জমা হয় 2 দিনে,
∴ 1200 টাকা জমা হয় = (2 × 1200)/150 = 16 দিনে
অর্থাৎ, 16 দিনের শেষে জমা থাকবে = 1200 টাকা
17-তম দিনে আবার আয় হবে = 300 টাকা
∴ মোট সঞ্চয় হবে = 1200 + 300 = 1500 টাকা
∴ 17-তম দিনে তার কাছে মোট 1500 টাকা জমা থাকবে।
0
Updated: 1 week 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
A can complete a piece of work in 36 days, B in 54 days and C in 72 days. All the three began the work together but A left 8 days before the completion of the work and B 12 days before the completion of work. Only C worked up to the end. In how many days was the work completed?
Created: 2 weeks ago
A
18 days
B
24 days
C
28 days
D
36 days
Question: A can complete a piece of work in 36 days, B in 54 days and C in 72 days. All the three began the work together but A left 8 days before the completion of the work and B 12 days before the completion of work. Only C worked up to the end. In how many days was the work completed?
Solution:
Let the work be completed in y days. C works for y days
Therefore, A works for (y - 8) days
B works for (y - 12) days.
According to the question,
{(y-8)/36} + {(y - 12)/54} + (y/72) = 1
⇒ 6(y - 8) + 4 (y - 12) + 3y = 216
⇒ 6y - 48 + 4y - 48 + 3y = 216
⇒ 13y = 216 + 96 = 312
⇒ y = 312/13
∴ y = 24
0
Updated: 2 weeks ago
