ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

Question: If 6 workers can build a wall in 10 days, how many workers would be needed to build the same wall in 5 days?

Solution: 
6 workers can build a wall in 10 days,
workers would be needed to build the same wall in 5 days = (6 × 10)/5 
= 12 workers

Question: 210 men working 12 hours a day can finish a job in 18 days. How many men are required to finish the job in 20 days working 14 hours a day?

Solution: 
210 men need (18 × 12) hours
= 216 hours

 to finish the job in 20 days working 14 hours a day men needed = (210 × 216)/(14 × 20)
= 162 

Question: 3 pumps, working 12 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?

Solution:
3 pumps need 2 days by working 12 hours
1 pump needs 1 day by working 12 × 3 × 2 hours
4 pumps need 1 day by working (12 × 3 × 2)/4 hours
= 18 hours

 

Question: Animesh takes twice as much as Bimol or thrice as much time as Rafi to finish a piece of work. Working together, they can finish the work in 3 days. Animesh can do the work alone in -

Solution:
Let, Animesh, Bimol, and Rafi take 6x, 6x/2 = 3x, and 6x/3 = 2x respectively.

Now, 
(1/6x) + (1/3x) + (1/2x) = 1/3
⇒ 6/6x = 1/3
⇒ 1/x = 1/3
⇒ x = 3

So, Animesh takes = 6 × 3 = 18 days

Question: A certain machine produces 1,000 units of product P per hour. Working continuously at this constant rate, this machine will produce how many units of product P in 7 days?


Solution:
7 days = 7 × 24 hours = 168 hours
In 1 hour, the machine produces 1,000 units
In 168 hours, the machine produces 1,000 × 168  units = 168000 units

Question:  Akash can do a piece of work in 30 days. He works at it for 6 days and then Rakib finishes it in 18 days. In what time can Akash and Rakib together finish the work?

Solution: 
আকাশ ৩০ দিনে করে সম্পূর্ণ অংশ 
১ দিনে করে ১/৩০ অংশ 
৬ দিনে করে ৬/৩০ অংশ 
= ১/৫ অংশ 

বাকি থাকে ১ - ১/৫ অংশ 
= ৪/৫ অংশ 

রাকিব ১৮ দিনে করে ৪/৫ অংশ 
১ দিনে করে ২/৪৫ অংশ 

রাকিব ও আকাশ ১ দিনে করে ১/৩০ + ২/৪৫ অংশ 
= ৩ + ৪/৯০ 
= ৭/৯০ 

সম্পুর্ণ কাজ করতে সময় লাগে = ৯০/৭ দিন 

Question: Abir does 80% of a work in 20 days. He then calls in Belal and they together finish the remaining work in 3 days. How long Belal alone would take to do the whole work?

Solution: 
abir does 80% or 4/5 work in 20 days 
in one day, he does 1/25 work 
in 3 days, he does 3/25 work 

work remaining = 1/5  - 3/25
= 2/25 work

Belal does 2/25 parts in 3 days 
he will complete the work 75/2 days

Question: Mr. Pollob can do a job in 120 minutes, while his colleague can do the same job in 3 hours. How long will it take them to work together to finish the same job?

Solution:
Mr. Pollob can do a job in 120 minutes = 2 hours
∴ Mr. Pollob can do in 1 hour = 1/2 portion of the job

His colleague can do in 1 hour = 1/3 portion of the job

Together they can do in 1 hour = 1/2 + 1/3 = 5/6 portion of the job

∴ Together they can do full job in (6/5) hour = (6 × 60)/5 minutes
= 72 minutes

Question: A worker was hired for 7 days. Each day, he was paid Tk. 10 more than what he was paid for the previous day of work. The total amount he was paid in the first 4 days of work equaled the total amount he was paid in the last 3 days. What was his starting pay?

Solution: 
ধরি,
১ম দিন ছিলো x টাকা 

২য় দিন = x + 10
৩য় দিন = (x + 20)
৪র্থ দিন = (x + 30)
৫ম দিন = (x + 40)
৬ষ্ঠ দিন = (x + 50) 
৭ম দিন = (x + 60) টাকা

প্রশ্নমতে,
x + (x + 10) + (x + 20) + (x + 30) = (x + 40) + (x + 50) + (x + 60)
⇒ 4x + 60 = 3x + 150
⇒ 4x - 3x = 150 - 60
∴ x = 90

Question: A map has a scale of 1 cm to 3 km, what length on actual ground does a 3 cm length on the map represent?

Solution: 
Given that,
1 cm represents 3 km 
∴ 3 cm represent (3 × 3) km 
= 9 km

Question: A works twice as fast as B. If B can complete a work in 12 days immediately, the number of days in which A and B can together finish the work- 

Solution:
B can complete a work in 12 days
So, A can complete the work in 6 days  

(A + B)'s 1 days work = (1/6 + 1/12) = 1/4 part
So, (A + B) can complete the work in 4 days

Question: Rabbi's regular pay is 30 Taka per hour up to 40 hours. Overtime is twice the payment for regular time. If he was paid 1680 Taka, how many hours of overtime did Rabbi work?

Solution:
40 ঘন্টার জন্য রাব্বির নিয়মিত বেতন = (30 × 40) = 1200 টাকা।
Overtime এর টাকার পরিমান = (1680 - 1200) টাকা = 480 টাকা
যেহেতু, Overtime এর প্রতিদিনের টাকার পরিমান নিয়মিত বেতন এর দ্বিগুন,
সেহেতু মোট overtime কাজ করার সময় = 480 ÷ (30×2) ঘন্টা = 8 ঘন্টা।

Question: P, Q, and R can do a job in 12 days together.  If their efficiency of working be in the ratio 3 : 8 : 5, Find in what time Q can complete the same work alone.

Solution: 
Given the ratio of efficiencies of P, Q & R are 3 : 8 : 5
Let, the efficiencies of P, Q & R be 3x, 8x and 5x respectively

They can do work for 12 days.
⇒ Total work = 12 × 16x = 192x


∴ The required time taken by Q to complete the job alone = 192x/8x
= 24 days.

Question: Sumi can type 10 pages in 5 minutes. Maria can type 5 pages in. 10 minutes. Working together, how many pages can they type in 30 minutes?

Solution:
Sumi can type in 1 min = 10/5 = 2 pages 
Maria can type in 1 min = 5/10 = 1/2 page

Working together they can type in 1 min = (2 + 1/2) pages 
= 5/2 pages 

∴ They can type in 30 min = (5 × 30)/2 pages
= 75 pages

Question: A carrier can carry 1.5 tons of products in 1 day from Teknaf to Tetulia. How much time will it be required to transfer 3 tons in two carriers?

Solution: 
১ টি কেরিয়ার ১.৫ টন মাল বহন করতে সময় নেয় ১ দিন
২ টি কেরিয়ার ৩ টন মাল বহন করতে সময় নেয় = (১.৫ × ২)/৩ = ১ দিন

Question: A pump removes water at a rate of 6 gallons per minute. How many hours will it take to remove 1800 gallons?

Solution:
Required time = 1800/6 mins 
= 300/60 hours
= 5 hours