ONE BANK LTD | PROBETIONARY OFFICER | WRITTEN QUESTION SOLVE(MATH)

Ashifur August 8, 2023 - 07:19

Question 1:

Three workers can do a job in 20 days. Two of the workers work twice as the third. How long would it take if one of the faster workers to do the job himself?

Answer:

One of the faster workers can do thejob in 50 days.

Explanation:

Let, each of the faster workers can do the job in x days
Slower worker can do the job in 2x days.
3 workers in one day can do = $\frac{1}{x}$ + $\frac{1}{x}$ + $\frac{1}{2x}$ portion
= $\frac{5}{2x}$ portion

3 workers In 20 days can do $\frac{5}{2x}$ x 20 — $\frac{50}{x}$ Portlon
$\frac{50}{x}$ =1
x = 50

Question 2:

In the figure below, ABC is a right angle triangle and AB = BD = AD = 20 feet. Find out the length of BC.

Answer:

$20\sqrt{3}$ ft

Explanation:

$\Delta$ ABD is a equal side triangle
$\angle$ ADB = 60°
$\angle$ BAD = 60°
$\angle$ DBC = 30° & $\angle$ BDC = 120°
$\angle$ DCB = 30°
in $\Delta$ BDC, $\angle$ DBC = $\angle$ DCB
BD = DC = 20
AC=AD+DC=20+20=40
ABC is a right triangle, AC is hypotenuse
AC² = AB²+ BC²
BC² = AC² — A8² = 40²-20² = 1200

BC = $\sqrt{400×3} =20\sqrt{3}$

Question 3:

Mr. X sold 2 properties, P1. and P2 for Tk. 1,00,000 each. He sold property P1 for 20% less than what he paid for it. What is the percentage of profit of property P2 so that he is not in gain or loss, on the sale of the two properties?

Answer:

$31\frac{1}{3}$ %

Explanation:

As property P.1 is 20% less than purchase price,
Purchase ofP1= 100000 x $31\frac{100\%}{80\%}$
= Tk. 125000
Loss = Tk. 25000
Mr X made profit from P2 = Tk. 25000
The purchase price of P2 was = Tk. 100000 — Tk. 25000
= T k. 75000
Profit in P2 was = $31\frac{25000}{75000}x100$ = $31\frac{1}{3}$ %

Question 4:

$\frac{2}{x-2}+\frac{3}{x+3}=1$

Answer:

$2\pm \sqrt{10}$

Explanation:

$\frac{2}{x-2}+\frac{3}{x+3}=1$
=> $\frac{2x+6+3x-6}{(x-2)(x+3)}=1$
=> $\frac{5x}{x^{2}+x-6}=1$
=> $x^{2}+x-6 = 5x$
=> $x^{2}-4x-6 = 0$
=> $x = \frac{-(-4)\pm \sqrt{(-4)^{2}-4x1x(-6)}}{2×1}$

=> x = $2\pm \sqrt{10}$

Question 5:

A labor is paid Tk. 8 per hour for an 8 hour day and $1\frac{1}{2}$ times that rate for each hour in excess of 8 hours in a single day. If the labor received Tk. 80 for a single day’s work, how long did he work on that day?

Answer:

$9\frac{1}{3}$

Explanation:

In first 8 hours he gets = Tk. 8 x 8 =TK 64

He gets from ever time = Tk. (80 – 64) = Tk. 16

Overtime (excess of 8 hours duty) rate = Tk. $8\frac{3}{2}$ = Tk. 12 per hour
Overtime = $\frac{16}{12}$ = $\frac{4}{3}$ hours

Total time he works = (8 + $\frac{4}{3}$ ) hours = $9\frac{1}{3}$ hours

Question 6:

Simplify the following algebraic expression. $\frac{9(4^{x})^{2}}{16^{x+2} -2^{x+1}(8^{x})}$

Answer:

$\frac{9}{254}$

Explanation:

Question 7:

200 children came to the park last Sunday. All of the older children rode bicycles into the park and all of the younger children came on tricycles. 480 Wheels rode into the park that day, all of them functioning on the children’s bicycles of tricycles. How many younger children came to the park last Sunday?

Answer:

Explanation:

Let, Number of older children = x

Number of younger children = (200 – x)

x x 2 + 3(200 —x) = 480

2x+600—3x=480

x = 120

Number of younger children = (200 — 120) = 80

Question 8:

Mr. A deposited a certain amount of money for a fixed period of time. On maturity, he received a total of Tk. 45000 and the ratio of interest and investment was 3:6. If the interest rate was 5% (simple) calculate the time period for which the money was invested?

Answer:

10 years

Explanation:

Here,

R = 5?

T =?

l= 15000Tk.
P = 30000Tk.
A = 45000Tk.

Let,
Interest be, I = 3x
and investment be, P = 6x
Amount be, A = 3x + 6x = 9::
According to the question,
9x = 45000

x = $\frac{45000}{9}$ = 5000 Tk
Interest, 1 = 3x = 3 x 5000 = 15000Tk
Investment, P = 6x = 6 x 5000 = 30000Tk
We know,

T = $\frac{100xI}{PR}$

= $\frac{100×15000}{30000×5}$ =10

Question 9:

A is two years older than B, who is twice as old as C. If the average age of the three is 9 years, how old is B?

Answer:

Explanation:

Let, the age of C = x

The age ofB = 2::

The age ofA =2x+ 2

According to the question,

$\frac{x+2x+2x+2}{3}=9$

=> 5x+ 2 =27

=> 5x=27—2

=> 5x=25

=> x=5

Now, Age of Be will be = 2x years
=2×5 =10

Three workers can do a job in 20 days. Two of the workers work twice as the third. How long would it take if one of the faster workers to do the job himself?

In the figure below, ABC is a right angle triangle and AB = BD = AD = 20 feet. Find out the length of BC.

Mr. X sold 2 properties, P1. and P2 for Tk. 1,00,000 each. He sold property P1 for 20% less than what he paid for it. What is the percentage of profit of property P2 so that he is not in gain or loss, on the sale of the two properties?

$\frac{2}{x-2}+\frac{3}{x+3}=1$

A labor is paid Tk. 8 per hour for an 8 hour day and $1\frac{1}{2}$ times that rate for each hour in excess of 8 hours in a single day. If the labor received Tk. 80 for a single day’s work, how long did he work on that day?

Simplify the following algebraic expression. $\frac{9(4^{x})^{2}}{16^{x+2} -2^{x+1}(8^{x})}$

Mr. A deposited a certain amount of money for a fixed period of time. On maturity, he received a total of Tk. 45000 and the ratio of interest and investment was 3:6. If the interest rate was 5% (simple) calculate the time period for which the money was invested?

A is two years older than B, who is twice as old as C. If the average age of the three is 9 years, how old is B?

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