Uttara Bank PLC || Probationary officer (23-11-2024) || 2024

1.

A businessman agrees to pay a debt of Tk. 20,000 with 10% compound interest. After how many years he will pay total amount of Tk. 51,874.85.

Here, C = P (1 + r)ⁿ

51874.85 = 20000 (1 + r)ⁿ

$S o, {(1 + \frac{10}{100})}^{n} = \frac{51874.85}{20000} = 2.59374$

So, ${(\frac{11}{10})}^{n} = {(\frac{11}{10})}^{10}$

so, n = 10

Required time = 10 Years (Ans)

In a factory, 60% workers like tea, and 30% workers like tea but not coffee. Find the number of workers:

2.

Who like both the drinks?

Here, Applying 2 by 2 Matrix Concept,

	T	T'
C	30	40
C'	30	0	30
	60	40	100

So, Number of Workers Like Both the Drink=30 (Ans)

In a factory, 60% workers like tea, and 30% workers like tea but not coffee. Find the number of workers:

3.

Who like coffee but not tea assuming 100% workers like either tea or coffee?

	T	T'
C	30	40
C'	30	0	30
	60	40	100

So, Number of Workers Like Coffee but not Tea =40 (Ans)

4.

In a class, if 4 students sit in each bench, 3 benches remain empty. But if 3 students sit in each bench, 6 students do not get any seat. Find the total number of students.

Let, Number of Benches be x

Atq, 4(x - 3) = 3x + 6

⇒ 4x - 12 = 3x + 6

⇒ x = 18

So, Number of Students = 18 $\times$ 3 + 6 = 60 (Ans)

5.

The ratio of prices of two houses was 16:23. Two years later when the prices of the first had risen by 10% and that of second by Tk. 477, the ratio of their prices become 11:20. Find the original prices of the two houses.

Here, Applying Ratio Adjustment Concept,

Initially, Price Ratio=16:23=160:230

Finally, Price Ratio=11:20=176:320

Now, 90 unit = 477 Tk.

390" = 2067 Tk.

Then, the original Prices of the two houses=2067 Tk. (Ans)

6.

Twenty years ago, the father's age was 4 times the age of his son, 4 years hence the father's age 2 times the age of his son. Find the present age of the father and the son.

Here, Let Present age of Father be F and Son be S

Atq, (F - 20) = 4(S - 20)

So, F - 4S =-60....(i)

Again, (F + 4) = 2(S + 4)

So, F = 2S + 4 (ii)

From Equation (i) and (ii) we Get,

2S + 4 - 4S = - 60

So, $S = \frac{64}{2} = 32 Y e a r s$

And, F = 2S + 4 = 2 $\times$ 32 + 4 = 68 years

So, Present age of father=68 Years (Ans)

And, Present age of Son=32 Years (Ans)

7.

Three persons buy cold drinks of different bands A, B, C. The first person buys 12 bottles of A, 5 bottles of B, 3 bottles of C. The second person buys 4 botties of A, 6 bottles of B and 10 bottles of C. The third person buys 6 bottles of A, 7 bottles of B and 9 bottles of C. If each bottle of brand A costs tk. 4, each bottle of B costs tk. 5 and each bottle of C costs 6, then find the total sum of money spent individually by three persons for the purchase of cold drinks.

First Person Spent:

(12 $\times$ 4) + (5 $\times$ 5) + (3 $\times$ 6) = 91Tk (Ans)

Second Person Spent:

(4 $\times$ 4) + (6 $\times$ 5) + (10 $\times$ 6) = 106Tk (Ans)

Third Person Spent:

(6 $\times$ 4) + (7 $\times$ 5) + (9 $\times$ 6) = 113Tk (Ans)

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Uttara Bank PLC || Probationary officer (23-11-2024) || 2024

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