DUTCH BANGLA BANK | PROBETIONARY OFFICER | WRITTEN MATH SOLVE

Ashifur August 8, 2023 - 14:29

Question 1:

A road was constructed along the fence of a rectangular plot, measuring 20 ft. long and 16ft. wide. The width of the road was 2 ft. Trees were planted 2 ft. apart on both sides of the road. How many trees were planted?

Answer:

88 Trees

Explanation:

The perimeter of the rectangular plot = 2(20 + 16) ft =72 ft

Number of trees =$\frac{72}{2}$ = 36

Again, The perimeter of the rectangular including the road= 2 {20 + (2 x 2) + 16 + (2 x 2)} ft
= 88ft
Number of Trees = $\frac{88}{2}$= 44
Number of total Trees = (36 + 44) = 80

Question 2:

On an average, Dr. X attends 12 patients per day and Dr. Y attends 16 patients per day. Dr. X’s charge is gtimes as much as that of Dr. Y. If Dr. Y earns Tk. 72,000 per month (30 days), what is the monthly income of Dr. X?

Answer:

TK 81000

Explanation:

Let, Dr. Y’s per patients charge = .1:

Dr. X’s patients charge = $\frac{x \cdot 3}{2}$

Now, Dr. Y’s monthly income = x x 16 x 30 = 480x

And Dr. X’s, monthly income =$\frac{x \cdot 3 \cdot 12 \cdot 30}{2}$ = 540x
480x = 72,000

x = 150

The monthly income of Dr. X = (540 x 150) = ‘TK. 81,000

Question 3:

There were some chocolates in a Box. Sami took $\frac{1}{4}$th of the chocolates; Arif took $\frac{1}{3}$rd of the remaining chocolates. Babu took $\frac{1}{2}$ of the chocolates left. Then Misha took 6 all that were left in the box. How many chocolates were there in the box?

Answer:

Total chocolates = 24

Explanation:

Let, total chocolates = x
Sam took = $\frac{1}{4}$ of x
The remaining chocolates = x —$\frac{1}{4}$
= $\frac{3x}{4}$
Arif took = $\frac{1}{3}$ of $\frac{3x}{4}$
= $\frac{x}{4}$
The remaining chocolates = $\frac{3x}{4}$ – $\frac{x}{4}$
= $\frac{x}{2}$
Babu took = $\frac{1}{2}$ of $\frac{x}{2}$
= $\frac{x}{4}$
The remaining chocolates = $\frac{x}{2}$ – $\frac{x}{4}$
=$\frac{x}{4}$
Misha took = $\frac{x}{4}$ = 6
x = 24

Question 4:

Four persons, each of whom works at the same rate, were to complete a job according to a schedule. However, because of a argument, two of the 4 quit after working for 1 day. The remaining persons finished the job, but it required 2 more days than what had originally been scheduled. How many days were originally scheduled for completion of the job?

Answer:

4 days

Explanation:

Let, the total time = x days
4 person 1 day work = $\frac{1}{x}$ portion
The remaining work = (1 – $\frac{1}{x}$) = $\frac{x-1}{x}$Portion
Again, 4 persons 1 day work =$\frac{1}{x}$ portion
2 persons 1 day work = $\frac{1 \cdot 2}{x . 4}$ Portion
2 persons (x+2) day work = $\frac{x+2}{2x}$ Portion

According to question , $\frac{x-1}{x}$ = $\frac{x+2}{2x}$

2x-2=x+2
x=4

Question 5:

Mr. Arif had traveled one-third the total distance when his car broke down. lie finished the journey on foot, spending 20 times as long walking as he had spent driving. If his average walking speed was 5 km/ hr, what was his average driving speed?

Answer:

50 km/hr

Explanation:

Let, the total distance = x kms
And time taken (t) hr by driving car
The distance traveling by car = x $\cdot \frac{1}{3}$ km
The distance traveling on foot = x – $\frac{x}{3}$ km
Time taken traveling on foot = (20 x t) hr. = 20t hr.
The distance travelling on foot = (5 x 20t) km = 100t
100t = x – $\frac{x}{3}$ km

100t = $\frac{2x}{3}$ $\frac{2 x}{3}$

x= 150t

The distance by travelling car = $\frac{150t}{3}$ = 50t

The average driving speed = $\frac{50t}{t}$ = 50 km/hr.

Question 6:

You can now buy 4 meters of more cloth with Tk. 800 because of a reduction in price by 20%. Calculate the original price and current price of per meter of cloth.

Answer:

The original price Tk. 50 and the current price Tk. 40.

Explanation:

In Tk. 100 decreases = Tk. 20
In Tk. 800 decreases = Tk.$\frac{20 \cdot 800}{100}$
= Tk. 160
The current price of 4 meters is Tk. 160
The current price of per meters is Tk. (160 / 4) = Tk. 40
At a reduction in price by 20%,
The current price = Tk. (100 — 20) = Tk. 80
The original price of per meter of cloth = $\frac{100 \cdot 40}{80}$ = Tk. 50

A road was constructed along the fence of a rectangular plot, measuring 20 ft. long and 16ft. wide. The width of the road was 2 ft. Trees were planted 2 ft. apart on both sides of the road. How many trees were planted?

On an average, Dr. X attends 12 patients per day and Dr. Y attends 16 patients per day. Dr. X’s charge is gtimes as much as that of Dr. Y. If Dr. Y earns Tk. 72,000 per month (30 days), what is the monthly income of Dr. X?

There were some chocolates in a Box. Sami took $\frac{1}{4}$th of the chocolates; Arif took $\frac{1}{3}$rd of the remaining chocolates. Babu took $\frac{1}{2}$ of the chocolates left. Then Misha took 6 all that were left in the box. How many chocolates were there in the box?

Mr. Arif had traveled one-third the total distance when his car broke down. lie finished the journey on foot, spending 20 times as long walking as he had spent driving. If his average walking speed was 5 km/ hr, what was his average driving speed?

You can now buy 4 meters of more cloth with Tk. 800 because of a reduction in price by 20%. Calculate the original price and current price of per meter of cloth.

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