রূপালী ব্যাংক সিনিয়র অফিসার লিখিত গণিতগুলোর বিস্তারিত সমাধান

Published Date: Saturday, January 4, 2020

রূপালী ব্যাংক সিনিয়র অফিসার ২৮৩ পোস্ট পরীক্ষায় আসা লিখিত গণিতগুলোর বিস্তারিত সমাধান
A) A basin can be filled tap A in 5 hours and by tap B in 8 hours, each tap working on its own. When the basin is full and a drainage hole is open, the water is drained in 20 hours. If initially basin was empty and someone started the taps together but the drainage hole open, how long does it take for the basin to be filled?
Solution:
Tap A can fill in 1 hours = 1/5 parts
Tap B can fill in 1 hours = 1/8 parts
& the drainage can empty in 1 hours=1/20parts
Tap A, Tap B and drainage can fill in 1hour
= 1/5 + 1/8 – 1/20
= (8 + 5 – 2)/40
= 11/40 parts
Full basin can be filled= 40/11 hrs =3(7/11)hrs (Answer)

B) A circular garden is surrounded by a road. If the outer circumference of the road is greater than the inner circumference by 88 meters. What is the width of the road?
Solution:
Radius of the circular garden= r meters
Radius of the garden with road= R meters
width of the road = (R- r) meter
Circumference of the garden = 2πr
Circumference of the garden with road = 2πR
According to the question,
2πR – 2πr = 88
=> 2π(R – r) = 88
=> (R – r) = 88/2π
=> (R-r)=88*7/2*22 [ π=22/7]
So, width of the road = 14 meters (answer)

C) A micro-bus was hired at Taka 5500 to travel intercity. The fare is shared equally among the passengers on the day of travel, but due to absence of 5 passengers, the average fare of per person was doubled. How many people availed the service?
Solution:
Let, the total passenger=x
people availed the service=x-5
According to the question,
5500/(x-5) = 2*5500/x
Or, 1/(x-5) = 2/x
Or, 2x – 10 = x
Or, x = 10
people availed the service=10-5=5 (Answer).

D) If a – 1/a = 3, proved it, a^4 + 1/a^4 = 119.
Given,
a – 1/a = 3

L.H.S = a^4 + 1/a^4
= (a^2)^2+(1/a^2)^2
= (a^2+1/a^2)^2-2a*1/a
={(a)^2+(1/a)^2}^2-2
={(a-1/a)^2+2*a*1/a}^2-2
={(3)^2+2}^2-2
={9+2}^2-2
={11}^2-2
=121-2
=119
=R.H.S
So, L.H.S=R.H.S(Proved)

E) Sum of ages of mother and daughter is 60 years. 5 years ago, the ratio of their age was 4:1. What will be the ratio their age after 10 years?
Solution:
Let,
Present age of mother =x years
Present age of daughter =60-x years

According to the question,
(x-5):(60-x-5)=4:1
=> (x +5)/(55-x) = 4/1
=> x+5=220-4x
=> 5x=225
=> x = 45

mother age after 10 years= 45+10=55 years
daughter age = 60-45+10=25 years
So, the required ratio= 55:25 = 11:5 (answer)

বাংলাদেশ ব্যাংক অফিসার পোস্টের শট সাজেশন

F) In a boy’s school, if 5 students sit in every bench, 4 benches are empty. But if 3 students sit in every bench, 20 students are left standing, what is the number of benched in the class?
Solution:
Let, the number of student = x.
So, the number of bench = x/5+4
According to the question,
x/5+4=(x-20)/3
=>(x+20)/5=(x-20)/3
=>5(x-20)=3(x+20)
=> 5x-100=3x+60
=> 5x-3x=60+100
=> 2x=160
=> x=80
So the number of bench =80/5+4=16+4=20(Answer)

প্রবাসী কল্যান ব্যাংকে অফিসার পদের এমসিকিউ পরীক্ষার সমাধান

G) The sum of three times the smaller and four times the larger is 71 and twice the larger of two number is three more than five times the smaller. What are the number?
Solution:
Let, the smaller number be x
And the larger number be y.
According to the question,
3x+4y = 71 ——–(i)
And,
5x +3=2y
Or,
5x – 2y = -3 ——-(ii)
(i)*1 + (ii)*2, than we get,
3x+4y=71…..(iii)
10x-4y=-6….(iv)
(iii)+(iv)
13x=65
=>x=5
Putting the value of x in (i). we get
3*5+4y= 71
=>4y=71-15
=>y=56/4
=> y= 14
So, the small number is 5
and the larger number is 14 (ans).

Solved by Kabil Mahmud

English Grammer এর কিছু চমক লাগানো নিয়ম

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