#### Question Solution #### পূবালী ব্যাংক: সিনিয়র অফিসার, অফিসার ২০১৭ (গণিত)

29 May 2017

1.Two trains of equal length are running on parallel lines in the same direction at 46  kilometre/hour and 36 kilometre/hour. The faster train pass to the slowest train in 36 seconds. The length of each train is-

Ans:50 m

Let ,

the length of each train is x meter

Distance will be x+x = 2x

Relative Speed = 46-36 = 10 km/hr

= 10*(5/18) = 25/9 m/sec

Distance = Speed*Time

Here,

2x = (25/9) X 36

or,x= 50 (Ans)

2.A man buys tk 20 shares paying 9% dividend.  The man wants to have an interest of 12% on his money. The market value of each share is-

Ans: 15

It is known that the formula is:

(Dividend / market value) * face value = interest.

or,Dividend / market value = interest / face value.

or,Face value * dividend = market value * interest.

We put it up to this equation, become:

20 * 9% = x * 12%.

1.8 = x * 12%.

1.8/12% = x.

15 = x.

3. By selling an article for  TK 100  a man gains tk 15 . then his gain percentage is -

Here,

Selling Price = tk 100,

Gain=Tk 15,

So , Buying or cost price =tk(100-15)

=Tk 85,

therefore Gain % = `((15)/85x100)`%=`17(11)/17` %

4.The age of a man is 3 times the sum of the age of his  two sons. 5 years hence, his age will be double of the sum of the ages of his sons the father's present age is-

Ans:45

Let ,

the sum of present ages of the two sons be x yeaTaka

Then,

Father’s present age = 3x yeaTaka

Here,

(3x + 5) = 2 (x + 10)

=>3x + 5 = 2x + 20

=>x = 15.

Hence, Father’s present age = 45 yeaTaka 5. If   tk 64 amount to 83.20 in 2 years what will tk 86 amount  to in  4 years in the same rate percent per annum?

P=Taka 64,  S.I. = Taka (83.20 - 64) = Taka 19.20, T = 2 years

So, rate = ( 100 x 19.20 )/ (64 x 2) % = 15%

Now, P = Taka 86, R= 15%, T = 4 years

S.I. =  Taka ( 86 x 15 x 14 )/100= Taka 51.60

6. A train travels at an average 50 miles per hour for 2.5 hours and then Travels at a speed of 70 miles per hour for 1.5 hours How far did the train travel in the entire 4 hours ?

7.0.04 X ? = 0.000016

Ans:0.0004

8. How many times in a day are the hands of a clock in straight line but opposite in direction?

Ans:22

The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. (Because between 5 and 7 they point in opposite directions at 6 o'clcok only). So, in a day, the hands point in the opposite directions 22 times.

9. The sum of a number and its reciprocal is 1/8  of 34. what is the product of the number and its square root?

Ans:8

Explanation:

Let the number be x. Then,

x + 1/x = 34/8

8x2 - 34x + 8 = 0

4x2 - 17x + 4 = 0

(4x - 1)(x - 4) = 0

x = 4

required number = 4 * √4 = 4 * 2 = 8.

10. A sum of money invested at compound interest amounts to Taka 4624 in 2 years and 4913 in 3 years .The sum of money is

A sum of money invested at compound interest amounts to Rs 4624 in 2 yrs and Rs 4913 in 3 yrs. The sum of money is

Ans:4096 Taka

Explanation:

4913 = P [1 + r/100]3

4624 = P [1 + r/100]2

Divide both equations, find r

Put value of r in one of the equations to find P

11.if 75% of a number is added to 75. then the result is the number itself .  The some of the number is

Ans: 300

Here,

75% of x plus 75 = x

0.75x + 75 = x

Bring the variable terms to the left side of the equation by subtracting x from both sides.

-0.25x + 75 = 0

Bring the constant terms to the right side by subtracting 75 from both sides.

-0.25x = -75

Divide both sides by -0.25

x = 300

12. A rectangular field :be fenced on three sides leaving a side of 20 feet uncovered.if the area of the field is 680 square feet .how many feet of fencing will be required?

Ans:88 feet

We are given with length and area, so we can find the breadth.

as Length * Breadth = Area

=> 20 * Breadth = 680

Area to be fenced = 2B + L = 2*34 + 20

= 88 feet

13.  Two pipes A and B can fill a cistern in 12 minutes and 15 minutes respectively while a third pipe C can empty the full tank in 6 minutes .A and B are kept open for 5 minutes in the beginning and then C  is also open. In what time is the cistern emptied -

Ans:45 minute

Part filled in 5 min = 5 * (1/12 + 1/15) = 5 * 9/60 = 3/4

Part emptied in 1 min when all the pipes are opened = 1/6 - (1/12 + 1/15) = 1/60

Now, 1/60 part is emptied in 1min

∴ 3/4 part will be emptied in 60 * 3/4 = 45 min

14.  The least number which is a perfect square and is divisible by each of the number is 16,20 and 24 is-

he least number which is divisible by 16,2016,20 and 2424 would be the LCM of three number .

Ans:Here,

LCM (16,20,24)

=>4×2×2×5×3=>4×2×2×5×3

=> 4×4×5×3=240

Hence to make 240 a perfect square we need to multiply by 5×3 as they are not in pair.

=>240×5×3=>240×5×3

=>3600 15.  Gold is 19 times as heavy as water and copper is 9 times as heavy as water in what ratio should this be mixed to get an alloy r 15 times as heavy as water :

Ans:3:2

Let,

the mass of 1 volume unit of water be 1. Then 1 volume unit of gold has mass 19, and 1 volume unit of copper has mass 9.

Now let g be the volume of gold used, and let c be the volume of copper. The total mass divided by the total volume is the density.

(19g + 9c)/(g + c) = 15

19g + 9c = 15g + 15c

4g = 6c

2g = 3c

g/c = 3/2

The volume ratio is 3:2.

16. the smallest prime number is-

Ans:2

17.  X can do a piece of work in 40 days he works at it for 8 days and then why finished it in 16 days. How long will they take  together take to complete the work

Ans:13 (⅓) days

Here,

X can the work in 40 days. He works at it for 8 days and that means he's finished a fifth of the work (1/5).

Now Y took 16 days to finish the rest of the work, which means he finished 4/5 th of the work in 16 days and will take 16 * 5/4 = 20 days to finish the work on a whole.

X  finishes 1/40 th of the work in one day. Y  finishs 1/20 th of the work in one day.

Since they work together their speeds add up and the time take t to complete the entire work W will be:

t = W / (Speed of X + Speed of Y) = W / (W/40 + W/20) = 1/ (1/40 + 1/20)

= (40 * 20) / (40 + 20) = 800/60 = 40 / 3

18.  In a 300 m race A beats B by 22.5 metre or 6 seconds. B's time over the course is -

Ans: 80

B runs 22.5 m in 6 seconds

=> B runs 300 m in (6×300)/22.5 = 80 seconds

B's time over the course = 80 seconds

19.if the mean of 5 observations X, X + 2 ,X + 4, x + 6 and X + 8 is 11 then the mean of the last 3 observations is-

First, you need to solve for x:

(x + x + 2 + x + 4 + x + 6 + x + 8) / 5 = 11

x + x + 2 + x + 4 + x + 6 + x + 8 = 55

5x + 20 = 55

5x = 35

x = 7

Now, substitute for x in each of the last three terms:

x + 4 + x + 6 + x + 8 = (7 + 4) + (7 + 6) + (7 + 8) = (11) + (13) + (15) = 39 / 3 = 13

The mean is 13.

20. A,B,C started business with their investment in the ratio 1 :3 :5 .After 4 month A invested the same amount as before  and B as well as C withdrew half  of their investment .The ratio of their profit at the end of the year is-

Ans: 5:6:10

Let their initial investments be x, 3x and 5x respectively.

Then X : Y : Z = (x * 4 + 2x * 8) : (3x * 4 + 3x/2 * 8 ): (5x * 4 + 5x/2 * 8 )

= 20x : 24x : 40x

= 5 : 6 : 10 21. √(√176 + √2401)  is equal to-

Ans:15

22..  49 pumps can empty a reservoir n 6.5 days, working 8 hours a day . If 196 pumps are used for 5 hours each day ,then the same work will be completed in-

Ans: 2(⅗) day

Let,

the required number of days be x.

Then,

More pumps, Less days (Indirect Proportion)

Less working hrs / day, More days (Indirect Proportion)

Pumps =196 : 49

Working Hrs / Day =5 : 8 :: 13/2 : x 96 x 5 x x = 49 x 8 x 13/2 x = 49 x 8 x 13/2 x 1 / (196 x 5) x = 13/5 ∎StudyPress-এ রেজিস্ট্রেশন করবেন যেভাবে--

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