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Question: If 400 gm of sugar costs 60 taka, how many taka will 1.2 kg cost?
Solution:
400 gm চিনির দাম = 60 taka
∴ 1 gm চিনির দাম = 60/400 taka
= 3/20 taka
এখন, 1.2 kg = 1200 gm
∴ 1200 gm চিনির দাম = 1200 × (3/20) taka
= (1200 × 3)/20 taka
= 3600/20 taka
= 180 taka
Question: 24 workers can complete a construction job in 15 days, working 6 hours a day. How many additional workers are needed to complete the same job in 10 days, working 8 hours a day?
Solution:
দৈনিক 6 ঘণ্টা করে কাজ করে 15 দিনে শেষ করতে লোক লাগে 24 জন
∴ দৈনিক 1 ঘণ্টা করে কাজ করে 1 দিনে শেষ করতে লোক লাগে (24 × 15 × 6) জন
∴ দৈনিক 8 ঘণ্টা করে কাজ করে 10 দিনে শেষ করতে লোক লাগে (24 × 15 × 6)/(10 × 8) জন
= 27 জন
∴ অতিরিক্ত লোক লাগবে = (27 - 24) = 3 জন
Question: X is 50% more efficient than Y. How much time will they, working together, take to complete a job which Y alone could have done in 25 days?
Solution:
X, Y এর থেকে 50% বেশি দক্ষ।
⇒ X : Y = 150 : 100 = 3 : 2
Y এক দিনে কাজ করে = 2 ইউনিট
X এক দিনে কাজ করে = 3 ইউনিট
মোট কাজ = Y এর দৈনিক কাজ × Y এর দিন = 2 × 25 = 50 ইউনিট
একসাথে এক দিনে কাজ করে = 3 + 2 = 5 ইউনিট
তাহলে কাজ শেষ করতে সময় লাগবে = 50 ÷ 5 দিন = 10 দিন
∴ সুতরাং, X এবং Y একত্রে কাজটি শেষ করতে 10 দিন সময় নেবে।
Question: A farmer grows paddy on one acre and gets 400 kg of it. If each kilogram of paddy yields 700 grams of rice, how much rice does he get in total?
Solution:
1 কেজি ধানে চাল হয় = 700 গ্রাম
= 700/1000 কেজি
= 0.7 কেজি
∴ 400 কেজি ধানে চাল হয় = (400 × 0.7) কেজি = 280 কেজি
Question: If 12 workers can complete a project in 15 days, how many days will it take for 9 workers to complete the same project assuming they all work at the same rate?
Solution:
12 workers can complete work in 15 days
∴ 1 workers can complete work in = 12 × 15 days
∴ 9 workers can complete work in = (12 × 15)/9 days
= 20 days
It will take 9 workers 20 days to complete the same project.
Question: A man completes 5/8 of a job in 10 days. At this rate, how many more days will it takes him to finish the job?
Solution:
Work done = 5/8
Balance work = 1 - (5/8) = 3/8
Let the required number of days be x
Then,
(5/8) : (3/8) :: 10 : x
⇒ (5/8) × x = (3/8) × 10
⇒ x = (3/8) × 10 × (8/5)
∴ x = 6
Question: A team of 10 workers can complete a task in 6 days by working 4 hours per day. If the same task is assigned to 15 workers, how many hours per day should they work in order to finish it in 2 days?
Solution:
10 persons can do the work in 6 days by working 4 hours a day
∴ Total man-hours = 10 × 6 × 4 = 240 hours
Let the required hours per day for 15 persons to finish in 2 days = x hours
∴ Total man-hours = 15 × 2 × x = 30x
Equating total work:
30x = 240
⇒ x = 240/30
⇒ x = 8
∴ 15 persons need to work 8 hours per day to complete the work in 2 days.
Question: A man completes 1/8 of a job in 10 days. At this rate, how many more days will it take him to finish the job?
Solution:
Work done = 1/8
Balance work = 1 - (1/8) = 7/8
A man completes 1/8 of a job in 10 days
A man completes 1 part of a job in 10 × 8 days
= 80 days
∴ More days required = 80 - 10
= 70 days.
After 25 days, 35 men complete the work in 12 days.
Thus, 35 men can finish the remaining work in 12 days.
∴ 30 men can do it in (12 × 35)/30
= 14 days.
which is 1 day behind.
Time is taken in walking both the ways = 7 hours 45 minutes -------- (i)
Time is taken in walking one way and riding back = 6 hours 15 minutes ----------- (ii)
By the equation (ii) × 2 - (i), we have,
Time is taken by the man in riding both ways,
= 12 hours 30 minutes - 7 hours 45 minutes
= 4 hours 45 minutes.
Question: Rafi alone can complete a work in 10 days and Tareq alone can complete it in 15 days. Rafi and Tareq undertook to complete the work for Tk. 7500. With the help of Salman, they finished the work in 5 days. How much should Salman be paid?
Solution:
Rafi's 1 day work = 1/10
Tareq's 1 day work = 1/15
Rafi + Tareq + Salman's 1 day work = 1/5
∴ Salman's 1 day work = 1/5 - (1/10 + 1/15)
= (6 - 3 - 2)/30
= 1/30
Salman's 5 days work = 5 × 1/30 = 1/6
Salman completed 1/6 of the total work.
∴ He should be paid 1/6 of Tk. 7500
∴ Salman’s payment = 7500 × 1/6 = Tk. 1250
Question: Rubel can do a job alone in 12 days. He works for 8 days and then leaves, and Rajib finishes the remaining work in 7 days. How long would it take Rajib to do 3/7 of the work alone?
Solution:
রুবেল একা,
12 দিনে করতে পারে = 1 অংশ
∴ 8 দিনে করতে পারে = 8/12 = 2/3 অংশ
∴ অবশিষ্ট কাজ = 1 - (2/3) = 1/3 অংশ
হাবিব একা,
1/3 অংশ কাজ করে = 7 দিনে
∴ হাবিব 1 অংশ কাজ করে = 3 × 7 দিনে
∴ হাবিব 3/7 অংশ কাজ করে = (3 × 7 × 3)/7 দিনে
= 9 দিনে
As, R takes 40 days to complete the work, (P + Q) will take = 40/2 = 20 Days
R can do 1/40 part of the work in one day and (P + Q) can do 1/20 part of the work in a day.
So, in 1 day (P + Q + R) can do = (1/20 + 1/40) = (3/40) part of the work
∴ Days required to complete 1 or Total work is = 40/3 = 13(1/3) days
Question: A television service center can process 8 televisions in 18 minutes. How many televisions can it process in 3 hours at this rate?
Solution:
3 hours = 3 × 60 = 180 minute
In 18 minutes, the service center can process = 8 tv
In 1 minute, the service center can process = 8/18 tv
In 180 minutes, the service center can process = (8 × 180)/18 tv
= 80 tv
Pump A can empty the pool in 3 hours therefore the rate at which it empties is 1/3 pool/hour
Pump b can empty the pool in 2 hours therefore the rate at which it empties is 1/2 pool/hour.
If they work together, the resulting rate is the addition of both rates (1/3 +1/2)pool/hour = 5/6 pool/hour
Now we have the following: (5/6pool)/60min = 1pool/x
Or, x = 72minutes
Ratio of times taken by A and B = 100:130 = 10:13
Suppose B takes x days to do the work.
Then,
10:13 :: 23:x
⇒ x = (23 × 13)/10
⇒ x = 299/10
A's 1 day's work = 1/23
B's 1 day's work = 10/299
(A + B)'s 1day's work = 1/23 + 10/299
= 23/299
= 1/13
∴ A and B together can complete the work in 13 days.
Question: A alone can do a piece of work in 6 days, and B alone in 8 days. A and B undertook to do it for Tk. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
Solution:
C's 1 day's work = (1/3) - {(1/6) + (1/8)}
= (1/3) - (7/24)
= 1/24
Now,
A's wages : B's wages : C's wages = (1/6) : (1/8) : (1/24)
= (1/6) × 24 : (1/8) × 24 : (1/24) × 24
= 4 : 3 : 1
∴ C's share (for 3 days) = 3 × (1/24) × 3200
= 400 Tk.
Question: A can do a work in 8 days and B in 12 days. If they work on it together for 4 days, then the fraction of the work that is left is-
Solution:
A's 1 day's work = 1/8
B's 1 day's work = 1/12
∴ (A + B)'s 1 day's work = (1/8 + 1/12) part
= (3 + 2)/24 part
= 5/24 part
∴ (A + B)'s 4 day's work = (5/24 × 4) part
= 5/6 part
Therefore, Remaining work = (1 - 5/6) part
= 1/6 part
Question: A can complete a work in 24 days and B in 16 days. They work together for 6 days. How many more days will A take alone to finish the remaining work?
Solution:
A একা কাজটি করতে পারে = 24 দিনে
∴ A এর একদিনের কাজ = 1/24 অংশ
এবং,
B একা কাজটি করতে পারে = 16 দিনে
∴ B এর একদিনের কাজ = 1/16 অংশ
∴ A ও B একসাথে একদিনের কাজ = (1/24) + (1/16) = (2 + 3)/48 = 5/48 অংশ
তারা 6 দিনে একসাথে কাজ করে = 6 × (5/48) = 5/8 অংশ
বাকি কাজ = 1 - (5/8) = 3/8 অংশ
অতএব,
A, 1/24 অংশ কাজ করে 1 দিনে
∴ 3/8 অংশ কাজ করে = (24 × 3)/8 = 9 দিনে
অতএব, A একা বাকি কাজ শেষ করতে ৯ দিন লাগবে।
Question: In a factory, 10 machines can produce 10 toys in 10 minutes. How many minutes will it take for one machine to produce one toy?
Solution:
10টি মেশিন 10টি খেলনা তৈরি করে 10 মিনিটে।
1টি মেশিন 10টি খেলনা তৈরি করে = 10 × 10 মিনিটে
1টি মেশিন 1টি খেলনা তৈরি করে = (10 × 10)/10 মিনিটে
= 10 মিনিটে।
Question: A and B together can complete a work in 10 days. A alone can complete it in 30 days. If B works only for half a day daily, then in how many days will A and B together complete the work?
Solution:
দেওয়া আছে,
A ও B একসাথে কাজটি সম্পন্ন করে = 10 দিনে
সুতরাং, তাদের এক দিনের কাজ = 1/10 অংশ
A একা কাজটি সম্পন্ন করে = 30 দিনে
সুতরাং, A এর এক দিনের কাজ = 1/30 অংশ
অতএব, B এর এক দিনের কাজ = (A ও B এর একসাথে কাজ) - (A এর একা কাজ)
= 1/10 - 1/30 অংশ
= (3 - 1)/30 অংশ
= 2/30 অংশ
= 1/15 অংশ
B প্রতিদিন অর্ধেক দিন কাজ করলে, তার প্রতিদিনের কাজ হবে,
= (1/15)/2 অংশ
= 1/30 অংশ
এখন, A (পুরো দিন) এবং B (অর্ধেক দিন) একসাথে কাজ করলে তাদের প্রতিদিনের মোট কাজ হবে:
= (A এর এক দিনের কাজ) + (B এর প্রতিদিনের কাজ)
= 1/30 + 1/30 অংশ
= 2/30 = 1/15 অংশ
যেহেতু তারা প্রতিদিন কাজের 1/15 অংশ সম্পন্ন করে, তাই সম্পূর্ণ কাজটি সম্পন্ন করতে তাদের সময় লাগবে 15 দিন।
সুতরাং, তারা একসাথে 15 দিনে কাজটি সম্পন্ন করবে।
Take work done = 1
Let number of sailors who could not board = S.
So sailors who boarded = 2500 - S
∴ 2500 sailors x 40 days x 1 = (2500 - S) sailors x 50 days x 1
∴ S = 500 = Sailors who could not board the ship.
[Men = M; Days = D; Time/Hours = T; Work = W
M1D1T1W2 = M2D2T2W1
Note that - W2 is on left side and W1 is on right side]
Question: Rahim's regular pay is Tk 40 per hour up to 40 hours. Overtime is paid at twice the regular rate. If he was paid Tk 2400 in total, how many hours of overtime did he work?
Solution:
Rahim’s regular wage for 40 hours = (40 × 40) = 1600 Taka.
Amount earned from overtime = (2400 - 1600) Taka = 800 Taka.
Since the overtime rate is twice the regular hourly wage,
Total overtime hours worked = 800 ÷ (40 × 2) hours
= 800 ÷ 80
= 10 hours
Question: If a team of 5 workers can assemble a motorcycle in 6 hours, how many hours would it take a team of 10 workers to assemble the same motorcycle, working at the same constant rate?
Solution:
Given,
5 workers can assemble a motorcycle in 6 hours
∴ 1 worker can assemble a motorcycle in (6 × 5) = 30 hours
∴ 10 workers can assemble a motorcycle in 30/10 = 3 hours
= 3 × 60 minutes
= 180 minutes
Let, the first and 2nd worker need X days.
Third worker needs 2X days
ATQ, 1/X + 1/X + 1/2x = 1/12
or, (2 + 2 + 1)/2x = 1/12
or, x = 30
Question: Karim can complete 2/5th of a certain work in 4 hours. Rahim works three times as fast as Karim and finishes the remaining work. How many hours did Rahim work?
Solution:
ধরি, সম্পূর্ণ কাজ = 1 অংশ
করিমের কাজের পরিমাণ = 2/5 অংশ
সময় = 4 ঘণ্টা
∴ পুরো কাজ (1 অংশ) করতে করিমের সময় লাগবে = 4 ÷ (2/5)
= 4 × 5/2
= 10 ঘণ্টা।
এখন, রহিম যেহেতু করিমের চেয়ে তিনগুণ দ্রুত কাজ করেন, তাই পুরো কাজটি সম্পন্ন করতে তার এক-তৃতীয়াংশ সময় লাগবে।
∴ পুরো কাজ করতে রহিমের সময় = 10 ÷ 3 = 10/3 ঘণ্টা।
বাকি কাজের পরিমাণ = 1 - (2/5) = 3/5 অংশ।
সুতরাং, রহিমের 3/5 অংশ কাজ করতে সময় লাগবে = (10/3) × (3/5) ঘণ্টা
= (10 × 3)/(3 × 5)
= 30/15
= 2 ঘণ্টা।