২২২২১
If 3x + 2y=8 and 2x - y =3, find the value of 4y - 3x.
উত্তর
-2
সমাধান
Here,3x+2y=8 2x-y=3if we multiply equation 2 with 2 and add it with equation 1 then we get, 7x=14 or x=2now, 4-y=3 (by substituting x=2 in equation 2) or, y=1So, 4y-3x=4 - 3*2= -2
২২২২২
The scale of a local map is 1cm to 5km. An area is represented on the map by a rectangle of dimensions 5cm x 9cm. The actual area in km is-
উত্তর
1125
সমাধান
Here, 1cm ≡ 5km
Actual dimension = (5x5)km x (9x5)km = 25km x 45km
So, the actual area = 25 x 45 km2 = 1125 km2
২২২২৩
In a cash box, there are equal number of 10 paisa, 25 paisa and 50 paisa coins. If it contains Tk. 170, then what is the number of 10 paisa coin?
উত্তর
200
সমাধান
Let's assume that there are 'x' coins of each denomination (10 paisa, 25 paisa, and 50 paisa) in the cash box.The value of x 10 paisa coins = 0.10x TkThe value of x 25 paisa coins = 0.25x Tk The value of x 50 paisa coins = 0.50x TkSo we can write an equation as:0.10x + 0.25x + 0.50x = 170Simplifying this equation, we get:0.85x = 170Dividing both sides by 0.85, we get:x = 200Therefore, there are 200 coins of each denomination in the cash box, and the number of 10 paisa coins is also 200.
২২২২৪
Of the 65 families in a locality, 45 have children and 10 have retired individuals as members. Of the families, 8 have both children and retired individuals as members. How many of the families have neither children nor retired individuals as members?
উত্তর
18
সমাধান
Number of families having children or retired individuals or both = 45 + 10 - 8 = 47
So, number of families having neither children nor retired individuals = 65 - 47 = 18.
২২২২৫
A time-study specialist has set the production rate for each worker on a certain job at 22units every 3hours. At this rate what is the minimum number of workers that should be put on the job if at least 90units are to be produced per hour?
উত্তর
13
সমাধান
The rate for each worker can be expressed as 22/3 units per hour.
We can let n = the number of workers needed to produce 90 units per hour, and we have:
n(22/3) = 90
or,22n = 270
∴ n = 270/22 = 12.2,
so there must be at least 13 workers.(ans)
২২২২৬
In a shop, the cost of 5 shirt , 5pairs of trousers and 3 hats is tk.710. The cost of 11shirts , 11pairs of trousers and 8 hats is tk. 1590. What is the total cost of 1 shirt,1 pair of trouser and 1 hat?
উত্তর
Tk. 150
সমাধান
5 shirt , 5 pairs of trousers and 3 hats = 710 TK - - - - - (i)
Now, multiplying both sides by 2,
10 shirt , 10 pairs of trousers and 6 hats = 1420 TK - - - - - - - (ii)
Again, 11 shirt , 11 pairs of trousers and 8 hats = 1590 TK - - - - - - (iii)
Now, {(iii) - (ii)}>> 1 shirt , 1 pair of trousers and 2 hats = 170 TK - - - - - (iv)
{(iii)×5}>> 5 shirt , 5 pairs of trousers and 10 hats = 850 TK - - - - - - (v)
Now, {(v) - (i)}>> 7 hats = 140 TK
So, 1 hat = 140/7 = 20 TK
From (iv), 1 shirt , 1 pair of trousers and 1 hat = 170 - 20 = 150 TK
২২২২৭
In a class the average marks attained in an exam is 80. The average of students who scored below 75 is 65. The average of students who scored 75 or more is 90. If the total number of students in this class is 20, how many students scored 75 or more?
উত্তর
12
সমাধান
The total number of students in the class is 20.
So let the number of people having marks greater than or equal to 75 be ‘x’
so number of students below 75 will be be ‘20 - x’.
ATQ,
65*(20 - x) + 90*(x) = 80*20
= > 1300–65x + 90x = 1600
= > 25x = 300
= >x = 12
ans:12
২২২২৮
What is the minimum nuber of flowers that must be added to an existing stock of 966 flowers so that the total stock can be equally distributed among 6, 7, 8 or 9 persons?
উত্তর
42
সমাধান
LMC OF 6,7,8,9 = 540
Existing number = 966
so, Minimum number must be added = (1008 - 966) = 42
ans: 42
২২২২৯
If helal, xony and Labu sit,respectively , in the 3rd, 5th and 6th positions. Which of the following must sin in the seveenth position?
উত্তর
Zafar
২২২৩০
A cricket team has won 40games out of 60played.It has 30 more games to play.How many of these must the team win to make record 70% win for them?
উত্তর
25
সমাধান
মোট games = 60 + 32 = 92 টি
92 এর 70% = 92 এর 70/100 = 64.4
Team টিকে আরও জিততে হবে ( 64.4 - 40) টি = 25 টি