written math practice part-01

Written Math practice part-01

1. The tens digit is four times the ones digit in a certain number. If the sum of the digit is 10, what is the

number?

Solution:

Let, the number be (10X+Y)

So, Tens digit=X and ones digit=Y

According to the question,

X=4Y and X+Y=10

Solving two equation,

We get, Y=2 and X=8

The number is 82. (Ans)

2. An old fashion country school room has double desks. If each student in the class sits at a different

desk, there are 2 students without seats. If 2 students sit together at a double desk, there is one empty

desk. How many students and how many desks are there in the class?

Solution:

Let, the number of desk be x


2(x-1)=x+2

Or, 2x-2=x+2

Or, 2x-x=2+2

x=4

Desks=4 and Students = 4+2=6 (Ans)

3. Five times the sum of the digits of a two-digit number is 13 less than the original number. If you

reverse the digits in the two-digit number, four times the sum of its two digits is 21 less than the reversed

two-digit number. The difference of the original two-digit number and the number with reversed digits is?

Solution:

Let, units digit=y and tens digit=x

The number is (10x+y) According to the question,

(10x+y)-5(x+y)=13

Or, 10x+y-5x-5y=13

5x-4y=13...... (1) And,

(10y+x)-4(x+y)=21

Or, 10y+x-4x-4y=21

6y-3x=21......(2) Now, from (1) and (2),

we get, x=9 and, y=8.

So, the original number will be 108+8=98.

Reversed number=89

Difference of the original two-digit number and the number with reversed digits is 98-89=9 (Ans)

4. Two cars race around a circular track in opposite directions at constant rates. They start at the same

point and meet every 30 seconds. If they move in the same direction, they meet every 120 seconds. If the

track is 1800 meter long, what is the speed of each car?

Solution:

Let, speed of 1st car is X m/s

And speed of 2nd car is Y m/s


30X+30Y=1800.(i) 120X-120Y=1800..(ii) From (i) we get,

X=180030

30 ..(iii)

Put the value of X into equation (ii)

120180030Y

30 -120Y=1800

Or, 4(1800-30Y)-120Y=1800

Or, 7200-120Y-120Y=1800

Y=22.5 From equation (iii)=>

X=18003022.5

30

=37.5

Speed of the 1st car=37.5 m/s and 2nd car= 22.5 m/s (Ans)

5. Mr.Walker invested 30,000 in stocks and bonds and had a total return of $2880 in one year. If his stock

investment returned 10% and his bond returned 9%, then how much did he invest in each?

Solution:

Let, investment in stock = x, & investment in bond = 30000-x.


x10%+(30000-x)9% = 2880

Or, 0.1x+2700-0.09x = 2880

Or, 0.01x= 2880-2700

x=18000. So, investment in stock = 18000 & investment in Bond=30000-18000=12000. (Ans)

6. Ashley invested her savings in two investment funds. The amount she invested in Fund A was twice as

the amount she invested in Fund B. Fund A returned a 6% profit and Fund B returned a 7% profit. How

much did she invest in Fund A if total profit from the two funds was $1520?

Solution:

Let fund B=x and Fund A=2x


6% of 2x+ 7% of x=1520

Or, 0.062x+0.07x=1520

Or, (0.12+-.07) x=1520

Or, 0.19x=1520

Or, x=1520/0.19

x=8000 at 7% Fund B

2x=16000 at 6% Fund A (Ans)

7. Masum invested his savings in two investment funds. The amount he invested in fund A was 3x as

much as the amount he invested in fund B. Fund A returned a 7% profit and fund B returned a 2% profit.

How much did he invest in fund B, if the total profit from two funds together was $2070?

Solution:

Let, investment in A = 3x & in B =x.


7% of 3x+2% of x=2070

Or, 7

1003x+

2

100x=2070

Or, 21x+2x= 207000

x =9000. So, investment in B = $9000. (Ans)

8. A prize of $900 is to be shared between a certain numbers of people. If there were two more people in

the group the prize money each person received would be reduced by $75. How many persons were in the

original group?

Solution:

Let, people =x. and Total prize = 900.


900/x= 900/(x+2)+75

Or, 900/x- 900/(x+2) = 75

Or, 900x+1800900x

x(x+2)=75

Or, 75x(x+2)=1800

Or, x2+2x=24

Or, x2+6x-4x-24=0

Or, (x-4)(x+6)=0

x=4, -6 (is not acceptable). Total person is 4 (Ans)

9. A group of friends went to dinner and received a bill totaling $288. The group decided to treat two

people whose birthdays were that month and split the charges equally among the rest of the group. This

resulted in each person having to pay $4.80 more than each would have paid had the bill been split

equally among the entire group. How many people were in the dinner group?

Solution:

Let people be x.


288/x-288/(x+2) =4.80

Or, 288+576288

(+2)=4.80

Or, x(x+2)=576/4.80

Or, x2+2x-120=0

Or, (x-10)(x+12)=0

x=10, -12 (is not acceptable). So, total people =10+2=12 (Ans)

10. The length of a rectangle is twice its width. If the length is increased by 4 inches and the width is

decreased by 3 inches, a new rectangle is formed whose perimeter is 62 inches. What is the length of the

original rectangle?

Solution:

Let, width be X inches

Length be 2X inches. When the length is increased by 4 inches=2X+4

And the width is decreased by 3 inches=X-3

According to question,

2{(2X+4)+(X-3)}=62

Or, 2X+4+X-3=62/2

Or, 3X+1=31

X=10

The length of the original rectangle=210

=20 inches (Ans)

11. The average of three numbers is 135. The largest number is 180 and the difference of the other

numbers is 25. What would be the smallest number?

Solution:

Let one number be =x & the other number be =y.

Sum of two numbers = 1353-180= 225.

And different of two numbers= 25.

So, x+y =225 and x-y =25.

From these two equation, we get x = 125.

The smallest no. is 225-125 =100 (Ans)

12. A printer quotes a price of taka 7,500 for printing 1,000 copies of a book and Taka 15,000 for printing

2,500 copies. Assuming a linear relationship and 2,000 books are printed, find (a) the variable cost per

book, (b) the average cost per book and (c) the fixed cost.

Solution:

(a) 1000 copies need 7500Tk

2500 copies need 15000Tk

Extra 1500 copies need 7500Tk This 1500 copies are fixed cost free,

We can get variable cost per book=7500/1500

=5 Tk (Ans)

(b) As cost function is linear and total cost for printing first 1000 copies is 7500tk and the variable cost

for per book is 5 Tk.

So, more 1000 copies cost=51000

=5000Tk

To print 2000 books we need=(7500+5000)

=12,500Tk

Average cost=12,500/2000 =6.25tk (Ans)

(c) Fixed cost=(7500-5000)=2500Tk(Ans)

13. A person travels from x to y at a speed of 40km/h and returns by increasing his speed by 50%. What

is his average speed for both the trips?

Solution:

Here, Going speed = 40km/h and Coming speed = 401.5 = 60 km/h.

So average speed =24060

40+60

= 4800/100

= 48 km/h (Ans)

14. Malek spends 75% of his income. His income is increased by 20% and he increases his expenditure

by 10% .Calculate the percentage of his increased amount of savings? (Basic Bank Asst Officer 09)

Solution:

Let, Maleks income is =100 taka Expenditure =75% of 100

= 75

Savings =100 75=25 According to the question,

At 20% increase,

new income =100+20% of 100

= 120 taka

New expenditure =75+10% of 75

=82.5 taka

New Savings =120-82.5

= 37.5 taka

% of increased amount of savings =[(37.525)/25]100% =50% (Ans)

15. Two tanks, X and Y, are filled to capacity with jet fuel. Tank X holds 600 gallons more than tank Y.

If 100 gallons of fuel were to be pumped from each tank, tank X would then contain 3 times as much fuel

as tank Y. What is the total number of gallons of fuel in the two full tanks?

Solution:

Let, tank Y contains = p gallons and tank X contains = (p+600) gallons


p+600-100=3(p-100)

Or, p+500=3p-300

Or, 3p-p=500+300

p=400 gallons. Now, Y contains = 400 gallons and X contains =(400+600)=1000 gallons

So, (X+Y) or total number of gallons will be =(400+1000) gallons

=1400 gallons (Ans)

16. A shopkeeper lost 7.5% by selling an article. If he had bought it at 10% less and sold it for 31 taka

more, he would have gained 20%. Find the cost price of the article.

(NB PO 14)

Solution:

Let, cost price X tk.

Now,


92.5% of X+31=108% of X

Or, 1.08X-0.925X=31

X=200 The cost price=200 tk (Ans)

17. Two metals A and B are 900% and 200% respectively heavier than water. If there two metals make an

alloy which is 6 times heavier than water, what is the ratio of the two metals in the alloy?

Solution:

Let, A is mixed = p & B is mixed = q.


900p+200q=600(p+q)

Or, 900p+200q=600p+600q

Or, 300p=400q.

p:q = 4:3 (Ans)

18. A, B and C can do a piece of work in 16, 32, and 48 days respectively. They started working together

but C left after working 4 days and B 2 days before the completion of work. How many days it took to

complete the work?

Solution:

1st 4 days A, B & C can do=4(1/16 +1/32 + 1/48) part

= 4(11/96)

=11/24 part.

Last 2 days only A can do this work =2(1/16)

=1/8 part.

Let, A & B working together in X days.

So, in X days A & B work=x(1/16+1/32)

=3x/32 part.

Now,

3x/32=1-(11/24 +1/8)

Or, 3x/32=5/12

Or, 36x=160

x =4.445 days Total days=4+5+2

=11 days

20. In 2005, the number of pairs of the shoes that a company sold to retailers decreased by 20 percent,

while the price per pair increased by 20 percent from that of the previous year. The company's revenue

from sales of the shoes in 2005 was taka 300000. What was the revenue from the sale of the shoes in

previous year?

Solution:

Let, previous year,

Shoes sold = x & price per shoes=y.

So, in 2005,

(x- 0.20x) (y+0.20y)=300000

Or, 0.80x 1.20y=300000

xy = 312500 Total revenue= 3,12,500 Tk (Ans)

Edited by

Jafar Iqbal Gem

Special Thanks to

1. Boka Soka

2. Rejia Sultana Tumpa

3. Imran Hossain Emu

4. Shahid Mazumder

5. Kalponik Prem

written math practice part-01

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