IBA ফ্যাকাল্টি ভিত্তিক প্রস্তুতি

Question: Nehal's regular pay is Tk 25 per hour up to 40 hours. Overtime is twice the payment for regular times. If he was paid Tk 1800, how many hours overtime did he work?

Solution:
Nehal’s regular wage for 40 hours = (25 × 40) = 1000 Taka.
Amount earned from overtime = (1800 - 1000) Taka = 800 Taka.
Since the overtime rate is twice the regular hourly wage,
Total overtime hours worked = 800 ÷ (25 × 2) hours
= 16 hours.

Question: In a certain country, a person born every 8 seconds and a person dies every 12 seconds. Therefore, the birth and death rates amount for a population growth rate of one person every-

Solution:
Let,
x be the number of seconds for the birth of every new person.

We know,
Birth rate - Death rate = Population growth

ATQ,
⇒ 1 person/8 seconds - 1 person/12 seconds = 1 person/x seconds
⇒ (3 - 2) person/24 seconds = 1 person/x seconds
⇒ 1 person/24 seconds = 1 person/x seconds
∴ x = 24 seconds

Question: To complete a work, A takes 50% more time than B. If together they take 18 days to complete the work, how much time shall B take to do it?

Solution:
Let
B takes x days to complete the work
Then A will take 50% more i.e 150% of x days i.e 3/2x days.

So the one day work of A and B together will be
(1/x) + {1/(3/2x)} = 1/18
⇒ (1/x) + (2/3x) = 1/18
⇒ 5/3x = 1/18
⇒ x = 30

∴ B takes 30 days to complete the work.

Question: 40 workers can build 40 engines working 6 hours a day. How many workers need to be appointed extra to boost the production to double if they work 8 hours a days?

Solution:
6 hours to build 40 engines by 40 workers
1 hour to build 1 engine by = (40 × 6)/40 workers
8 hours to build 80 engine by = (6 × 80)/8 workers
= 60 workers

∴ extra workers = (60 - 40) = 20 workers

Question: A ferry can carry 30 buses or 48 cars at a time. If there are 20 buses on the ferry, how many cars can be loaded onto it?

Solution:
Here,
30 buses = 48 cars
∴ 1 bus = 48/30 cars
∴ 20 buses = (48 × 20)/30 cars
= 32 cars

∴ Required number of cars = 48 - 32 = 16 cars

Question: Sumi can type 75 pages in 25 minutes. Maria can type 5 pages in 15 minutes. Working together, how many pages can they type in 30 minutes?

Solution:
Sumi can type in 1 min = 75/25 = 3 pages
Maria can type in 1 min = 5/15 = 1/3 page

∴ Working together they can type in 1 min = (3 + 1/3) pages
= 10/3 pages

∴ They can type in 30 min = (10 × 30)/3 pages
= 100 pages

Question: Running at the same constant rate, 8 identical machines can produce a total of 320 bottles per minute. At this rate, how many bottles could 15 such machines produce in 6 minutes?

Solution:
Given,
In 1 minute, 8 machines can produce 320 bottles
In 1 minute, 1 machines can produce 320/8 bottles
So, in 6 minute, 15 machines can produce = (320 × 6 × 15)/8 bottles
= 3600 bottles

Question: A group of workers can do a piece of work in 24 days. However, as 7 of them were absent, it took them 30 days, to complete the work. How many people actually worked on the job to complete it?

Solution:
Let,
the total number of people were working originally = x
When 7 people were absent,
Total present workers were = x - 7

x workers can complete it = 24 days.
∴ 1 workers can complete it = 24x days.
∴ (x - 7) workers can complete it = 24x/(x - 7) days.

ATQ,
24x/(x - 7) = 30
⇒ 4x/(x - 7) = 5
⇒ 5x - 35 = 4x
∴ x = 35
The total number of people were working originally 35.

Question: If 7 workers can assemble a car in 8 hours, how long would it take 12 workers to assemble the same car?

Solution:
Given,
7 workers can assemble a car in 8 hours
∴ 1 workers can assemble a car in (8 × 7) hours
∴ 12 workers can assemble a car in (56/12) hours
= (56 × 60)/12 minutes
= 280 minutes

Question: A and B together complete a piece of work in x days. If A alone completes the work in x + 3 days and B alone completes the piece of work in x + 12 days, what is the value of "x"?

Solution:
A's 1 day's work = 1/(x + 3) part
B's 1 day's work = 1/(x + 12) part
and (A + B)'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

Question: Rasel can fill advertising circulars into envelopes at the rate of 45 envelopes per minute and Ali requires a minute and a half to fill the same number of envelopes. Working together, how long will it take Rasel and Ali to fill 300 envelopes?

Solution:
Given,
Rasel can fill 45 envelopes in 1 minutes
and,
Ali can fill 45 envelopes in (1 + 1/2) = 3/2 minutes
So Ali can fill in 1 minutes = (45 ÷ 3/2) envelopes
= (45 × 2/3) envelopes
= 30 envelopes

So Rasel and Ali together can fill in 1 minutes = (45 + 30) = 75 envelopes

∴ 75 envelopes can fill in 1 minutes
∴ 1 envelopes can fill in 1/75 minutes
∴ 300 envelopes can fill in (1 × 300)/75 minutes
= 4 minutes

Question: If Arif works alone he will take 20 more hours to complete a task than if he works with Babu to complete the task. If Babu work alone, he will take 5 more hours to complete the task than if he works with Arif to complete the task. What is the ratio of the time taken by Arif to than taken by Babu if each of them works alone to complete the task?

Solution:
ধরি
আরিফ ও বাবু কাজটি করে x ঘণ্টায়

আরিফ একা কাজটি করে (x + 20) ঘণ্টায়
বাবু একা কাজটি করে (x + 5) ঘণ্টায়

প্রশ্নমতে,
{1/(x + 20)} + {1/(x + 5)} = 1/x
⇒ 1/(x + 20) = (1/x) - {1/(x + 5)}
⇒ 1/(x + 20) = (x + 5 - x)/(x² + 5x)
⇒ 1/(x + 20) = 5/(x² + 5x)
⇒ x² + 5x = 5x + 100
⇒ x² = 100 
∴ x = 10

আরিফ একা কাজটি করে (10 + 20) ঘণ্টা = 30 ঘণ্টায়
বাবু একা কাজটি করে (10 + 5) ঘণ্টা = 15 ঘণ্টায়

আরিফ ও বাবুর কাজের সময়ের অনুপাত = 30 : 15
= 2 : 1

Question: Courier charges for packages to a certain destination are Tk. 95 for the first 300 grams and Tk 10 for each additional 100 grams or part thereof. What could be the weight in grams of a package for which the charge is Tk. 165?

Solution:
Let
the additional is 100x grams
Additional 100 grams requires Tk.10
∴ Additional 100x grams requires Tk. (10 × 100x)/100 = Tk. 10x

ATQ,
95 + 10x = 165
⇒ 10x = 70
∴ x = 7

∴ The additional weight = 100 × 7 = 700 grams
∴ Total weight will be = 700 + 300 = 1000 grams

Question: A can write 100 pages in 25 hours. A and B together can write 210 pages in 30 hours. In what time can B write 42 pages?

Solution:
Given,
In 25 hours A can write 100 pages
∴ In 1 hour A can write 100/25 pages
= 4 pages

Here,
∴ In 1 hour A and B together can write 210/30 pages
= 7 pages
and,
B's 1 hour work = (A + B)'s 1 hour work - A's 1 hour work
= 7 - 4
= 3 pages/hour

B's time
3 pages in 1 hour
∴ 1 page in 1/3 hour
∴ 42 pages in = (1 × 42)/3 hour
= 14 hours

Question: A man and a boy together can do a certain amount of digging in 28 days. Their speeds in digging are in the ratio of 7 : 4. How many days will the boy take to complete the work if engaged alone?

Solution:
Ratio of digging speeds of man and boy = 7 : 4
Ratio of times taken by man and boy = 4 : 7
Suppose the man takes 4x days while the boy takes 7x
∴ Man's 1 day's work = 1/4x part
∴ Boy's 1 day's work = 1/7x part

ATQ,
1/4x + 1/7x = 1/28
⇒ (7 + 4)/28x = 1/28
⇒ 11/28x = 1/28
⇒ 28x = 28 × 11
∴ x = 11

Hence, time taken by the boy to complete the work alone = (7 × 11) days
= 77 days