ব্যাংক ডেইলি কুইজ [লং কোর্সের অংশ]

Question:  If 3 spiders make 3 webs in 3 days, then 1 spider will make 1 web in how many days?

Solution: 
3 spiders can make 3 webs in 3 days,
3 spiders can make 1 webs in 3/3 days,
1 spiders can make 1 webs in (3 × 3)/3 = 3 days

Question: 18 men bind 900 books in 10 days. Find how many binders will be required to bind 600 books in 12 days?

Solution: 
To bind 900 books in 10 days binders needed 18 men 
To bind 1 books in 1 days binders needed 180/900 men 
To bind 600 books in 12 days binders needed (180 × 600)/(900 × 12) men
= 10 men

Question: Piyal and Belal together can complete a work in 3 days. They start together but after 2 days, Belal left the work. If the work is completed after two more days, Belal alone could do the work in how many days?

Solution:
(Piyal + Belal)'s one day's work = 1/3 part
(Piyal + Belal) works 2 days together = 2/3 part
Remaining work = 1- 2/3
= 1/3 part

1/3 part of work is completed by Piyal in two days
Hence, one day's work of Piyal = 1/6 part

Then, one day's work of Belal = 1/3 - 1/6 = 1/6
So, Belal alone can complete the whole work in 6 days.

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: If 8 men can reap 40 hectares in 12 days, then how many hectares can 30 men reap in 20 days?

Solution: 
8 men can reap  in 12 days 40 hectares
1 men can reap  in 1 days  40/(12 × 8) hectares
30 men reap in 20 days = (40 × 600)/96
= 250 hectares

Question: A garrison of ‘n’ men had enough food to last for 30 days. After 10 days, 50 more men joined them. If the food now lasted for 16 days, what is the value of n?

Solution: 
After 10 days, the food for n men is there for 20 days.
This food can be eaten by (n + 50) men in 16 days.

So,
20n = 16(n + 50)
⇒ 20n - 16n = 800
⇒ 4n = 800
∴n = 200

Question: Joy can knit a pair of socks in 3 days. Belal can knit the same pair of socks in 9 days. If they are knitting together, then in how many days will they knit two pairs of socks?

Solution: 
They knit in one day = (1/3) + (1/9)
= 4/9 days

They knit a pair of socks in 9/4 days
they knit two pairs of socks in (9 × 2)/4 days 
= 9/2 days

Question: An air conditioner can cool the hall in 40 miutes while another takes 60 minutes to cool under similar conditions. If both air conditioners are switched on at same instance then how long will it take to cool the room?

Solution: 
৪০ মিনিটে ঠান্ডা হয় সম্পূর্ণ অংশ 
১ মিনিটে পূর্ণ হয় ১/৪০ অংশ 


৬০ মিনিটে পূর্ণ হয় সম্পূর্ণ অংশ 
১ মিনিটে পূর্ণ হয় ১/৬০ অংশ  


দুটি মিলে পূর্ণ হয় ১/৪০ + ১/৬০ 
= ৩ + ২ / ১২০
= ৫/১২০ মিনিট 
= ১/২৪ মিনিট 

সম্পূর্ণ অংশ ঠান্ডা হতে সময় লাগে ২৪ মিনিট। 

Question: The mess charges for 35 students for 24 days in Tk 6300. In how many days will the mess charges be Tk 3375 for 25 students?

Solution: 
Let C be the daily mess charge per student.
Given that mess charges for 35 students for 24 days is Tk 6300, the daily cost per student is = 6300/(35 × 24)
= 7.5 

Now, to find how many days mess charges will be Tk 3375 for 25 students, we can use the daily cost per student (C):

The total mess charges for 25 students in D days is 3375 = 25 × C × D
⇒ D = 3375/(25 × 7.5)
= 18

Question: 76 ladies complete a job in 33 days. Due to some reason, some ladies did not join the work and therefore it was completed in 44 days. The number of ladies who did not report for the work is- 

Solution: 
Let L be the rate of work per lady. 

the total work = 76L × 33 

Let,  with x ladies absent, the total work is = (76 - x)L × 44

 76L × 33 = (76 - x)L × 44
⇒ 76 × 33 = 76 × 44 - 44L 
⇒ 44L = 76 × 44 - 76 × 33 = 76 × 11 
⇒ L = 19