বিগত সালের প্রশ্ন ও প্রশ্ন ব্যাংক
বিসিএস, ব্যাংক, প্রাথমিক শিক্ষক ও সকল সরকারি চাকরির বিগত সালের প্রশ্ন ও অধ্যায়ভিত্তিক নির্ভুল সমাধান
- ট্যাংকটি x ঘণ্টায় খালি হবে।
- ছিদ্র থাকা অবস্থায় পানি ভর্তি হতে সময় লাগে = (8 + 2) ঘণ্টা = 10 ঘণ্টা।
প্রশ্নমতে, : 1/8 - 1/x = 1/10
1/x = 1/8 - 1/10
1/x = (5 - 4) / 40
1/x = 1/40
x = 40
∴ x = 40 hours
Expression:
1 / (1/p + 1/q - 1/r)
1 / (1/p + 1/q - 1/r) = 1 / ( (qr + pr - pq) / pqr )
1 / ( (qr + pr - pq) / pqr ) = pqr / (qr + pr - pq)
∴ The simplified expression is: pqr / (qr + pr - pq)
Given:
- Time taken by Pipe P = 24 hours
- Time taken by Pipe Q = 72 hours (since Pipe Q takes 3 times more than Pipe P)
Time taken by both pipes together = (24 × 72) / (24 + 72)
Time taken by both pipes together = 1728 / 96 = 18 hours
∴ Time taken by both pipes to fill the tank is: 18 hours
Given:
- Pipe A alone takes x hours to fill the tank.
- Pipe B will take x/2 hours to fill the tank.
- Pipe C will take x/4 hours to fill the tank.
The rates of filling by each pipe are:
- Pipe A: 1/x
- Pipe B: 2/x
- Pipe C: 4/x
ATQ,
1/x + 2/x + 4/x = 1/5
7/x = 1/5
x = 35 hours
∴ The time taken by Pipe A alone to fill the tank is: 35 hours
Given:
- Principal (P) = Tk. 600
- Rate of Interest (r) = 10% = 1/10
- Time (n) = 2 years
Compound Amount Formula:
Compound Amount = P × (1 + r)^n
Substitute the given values:
Compound Amount = 600 × (1 + 1/10)^2
Compound Amount = 600 × (11/10)^2
Compound Amount = 600 × (11/10) × (11/10) = 726
∴ Compound Amount = Tk. 726
প্রদত্ত:
- প্রধান অর্থ (P) = Tk. 800
- সুদের হার (r) = 12.5% = 0.125
- সময় (n) = 9 মাস = 9/12 বছর
আমরা জানি:
I = P × n × r
⇒ I = 800 × (9/12) × 0.125
⇒ I = 800 × 0.75 × 0.125 = 75
∴ সুদ: Tk. 75
Given:
- Total money lent = Tk. 10,000
- Tk. 2,000 at 8%
- Tk. 4,000 at 7.5%
- Tk. 1,400 at 8.5%
- Average interest = 8.13%
Step 1: Remaining amount
Remaining = 10,000 - (2,000 + 4,000 + 1,400) = Tk. 2,600
Step 2: Interest from first three parts
- 2000 × 8% = 160
- 4000 × 7.5% = 300
- 1400 × 8.5% = 119
Total known interest = 160 + 300 + 119 = Tk. 579
Step 3: Total required interest (average 8.13%)
Total interest = 10000 × 8.13% = Tk. 813
So, interest needed from remaining = 813 - 579 = Tk. 234
Step 4: Find rate on remaining Tk. 2,600
(2600 × r) / 100 = 234
⇒ 26r = 234
⇒ r = 234 / 26 = 9%
∴ Required rate of interest = 9%
Solution:
Here,
P = M
r = M%
I = M
n = 4
We know that,
I = Pnr
M = M × 4 × (M/100)
⇒ 1 = M/25
∴ M = 25