Mercantile Bank Ltd

প্রশ্নঃ A rectangular area of 16 meters by 12 meters, is surrounded by a road 3 meters wide. The area of the road is :

বর্ণনাঃ

the length of the rectangular area plus the road on each end is =16 + (3*2) = 22 meters.

the width of the rectangular area plus the road on each end is= 12 + (3*2)= 18 meters.

the area of the rectangular area plus the width of the road is (22 * 18)= 396 square meters.

the area of the rectangular area by itself is (16 * 12)= 192 square meters.

the area of the road is the total area minus the rectangular area which is equal to (396 - 192)= 204 square meters.

ans: 204 sq meters

প্রশ্নঃ The width of a rectangular plot was reduced by 30% and the length was reduced by 10%. The size of the new plot is what percent of the original plot?

বর্ণনাঃ

Let the width and length be W & L respectively.

Then,  area = W x L

Width after 30% reduction = 0.7W

Length after 10% reduction = 0.9L

New area = 0.7W x 0.9L = 0.63 W x L (which is 63% of initial area)

প্রশ্নঃ If one angle of a triangle is three times a second angle and the third is 20 degrees more than the second angle, the second angle, in degrees, is

বর্ণনাঃ

Let, third angle be =x

Second angle =x-20

First angle=3( x-20) =3x-60

Sum of angles of triangle=180

Hence ATQ,

3x-60+x-20+x=180

or,5x-80=180

or,5x=180+80=260

or,x=260/5=52

.'.Second Angle=52–20 =32° (ans)

প্রশ্নঃ If m men can paint a house in d days, how many days will it take m+2 men to paint the same house?

বর্ণনাঃ

m men can paint a house in d days,  

.',1 men can paint a house in md days  

so, (m+2) men would finish the same job in = md/(m+2)

ans:  md/(m+2) 

প্রশ্নঃ If 3x+2>2x+7, then x is

বর্ণনাঃ

If 3x+2>2x+7

3x - 2x > 7 - 2 

x > 5 

প্রশ্নঃ Which of the following is the largest?

বর্ণনাঃ

12/15 = 0.8

  11/14 = 0.78571

  5/6  = 0.833 [ largest ] 

  15/20 = 0.75

প্রশ্নঃ If 89 and 125 is divided by a positive integer X, then the remainders are 4 and 6 respectively.

বর্ণনাঃ

প্রশ্নঃ It costs Tk. 1000 to make the first thousand copies of a book and x taka to make each additional copies. If a total of 6000 copies were made with a total cost of Tk. 5500, what is X?

বর্ণনাঃ

Cost of first thousand copies 1,000 Tk

Susbequent copies=(6000-1000)= 5000 copies

Cost of subsequent 5000 copies = 5500-1000 =4500tk .

According to ques,

5000x= 4500

X=4500/5000=0.9

ans: 0.9

প্রশ্নঃ If x is 2/5 of y and y is 5/7 of z, what is the ratio of z : x?

বর্ণনাঃ

According to the question,

X = 2Y/5

& Y = 5Z/7

=> X = 2/5 x 5Z/7

=> X = 2Z/7

=>Z/X = 7/2 = 7:2

Answer: 7:2

প্রশ্নঃ If 3 tailors can make 60 shirts per day, how many days will it take 6 tailors to make 120 shirts?

বর্ণনাঃ

3 tailors can stitch 60 shirts in 1 day 

1 tailors can stitch 60/3=20 shirts in 1 day

so 6 tailors can stitch=(6*20)= 120 shirts in 1 day

ans: 1 day

প্রশ্নঃ A trader purchased some pens for Tk. 150. If the price of each pen was Tk. 5 less, he would have got 5 more pens. How many pens did he buy?

বর্ণনাঃ

Let the number of pens bought by him be P.

Then, the price of each pen = 150/P

According to the question,

150/(P + 5) = (150/P) - 5

or,  (P + 5) x {(150/P) - 5} = 150

or, 150 - 5P + 750/P -25 = 150

or,  (750 - 5P²)/P = 25

or,  750 - 5P² = 25P

or,  5P² + 25P -750 = 0

or, P² + 5P -150 = 0

or, P² + 15P - 10P -150 = 0

or, (P + 15)(P - 10) = 0

So,   P = 10.

প্রশ্নঃ If a man was r years old s years ago, how many years old will he be t years from now?

বর্ণনাঃ

a man was r years old s years ago,so his present age is= r+s

after t years his age will be= r+s+t

ans: r+s+t

প্রশ্নঃ If A : B= 1 : 2, B : C = 4 : 3 and A + B + C = 450, what is the value of B?

বর্ণনাঃ

A : B= 1:2,= 2:4 (multiplying by 2)

B : C = 4:3 

so, we get. A:B:C= 2:4:3

let, A= 2x, B= 4x, C=3x

According to the Question,

A + B + C = 450

or, 2x+4x+3x= 450

or, 9x=450

or, x= 50

.'. B= 4x = 4*50= 200

ans: 200

প্রশ্নঃ The length of a rectangle is increased by 50%. By what percent would the width have to be decreased to maintain the same area?

বর্ণনাঃ

Let, the length of the rectangle be x cm and the breadth of the rectangle  y cm

Therefore area of the rectangle = x * y = xy cm²

as the length is increased by 50%

.'. length = x + 50% of x

            = x + 50/100 *x

            = x + x/2

            = 3x/2

Given that area is constant

so, xy = 3x/2 * breadth

breadth = 2xy/3x = 2y/3 cm

Percentage of increase in breadth = decrease in breadth/original breadth *100

                                                           = (y - 2y/3)/y * 100

                                                           =  ((3y - 2y) / 3)/y*100

                                                           = y/3y *100

                                                           = 100/3

                                                           = 33.333%

The breadth is decreased by 33.333% (Ans)

প্রশ্নঃ Three workers can do a job 12 days. Two of the workers work twice as fast as the third. How long would it take one of the faster workers to do the job alone?

বর্ণনাঃ

1 faster person = 2 slower person 

so , 2 faster +one slower = 5 slower person

 5 slower person can do the work in 12 days

1  slower person can do the work in (12X5) days= 60 day

as, 2 slower = 1 faster 

then , 2 slower or 1 faster person can do the work in 60/2 = 30 days

ans: 30 days

প্রশ্নঃ The length of a room is 1.5 times of its breadth. If the area of the room is 216 sq. meter, what is the perimeter of the room?

বর্ণনাঃ

let, the breadth is x 

so, tthe length is 1.5 x

Accoring to the question,

x*1.5x= 216

or, 1.5 x² =216

or, x= 12

breadth=12 m

length = 12* 1.5= 18

so, perimeter= 2(12+18) = 60 m

ans: 60 m