ব্যাংক ডেইলি কুইজ [লং কোর্সের অংশ]

Question: If 40% of a certain number is 14, then find the number-

Solution:
Let the number be x.
Then,
⇒ 40% of x = 14
⇒ (40/100) × x = 14
⇒ 2x/5 = 14
⇒ x = 70/2
∴ x = 35

Question: If a = 4, b = 6 and c = 3, then a(b - c)/b(a + b + c) =?

Solution:
Given that,
a = 4, b = 6 and c = 3

Now,
a(b - c)/b(a + b + c)
= 4(6 - 3)/6(4 + 6 + 3)
= 12/78
= 2/13

Question: If x = 3 - 5a and y = 2a + 3, then for what value of a, x is equal to y?

Solution:
Given that,
x = 3 - 5a
y = 2a + 3

Now,
x = y
⇒ 3 - 5a = 2a + 3
⇒ 5a + 2a = 3 - 3
⇒ 7a = 0
∴ a = 0

∴ The value of a is 0

Question: The sum of four consecutive even numbers is 140. What is the sum of next two consecutive even numbers-

Solution:
let, four consecutive even numbers is
x, x + 2, x + 4, x + 6

ATQ,
⇒ x + x + 2 + x + 4 + x + 6 = 140
⇒ 4x + 12 = 140
⇒ 4x = 140 - 12 = 128
⇒ x = 128/4
∴ x = 32

So four consecutive even numbers is- 32, 34, 36, 38

∴ next two consecutive even numbers- 40, 42
∴ sum = 40 + 42 = 82

Question: If a + b = 10 and ab = 21, then what is the value of a² + b² = ?

Solution:
Given that,
a + b = 10
ab = 21

We know,
a² + b² =(a + b)² - 2ab
= (10)² - (2 × 21)
= 100 - 42
= 58

Question: The price of 6 notebooks is equal to the price of 2 calculators. The total price of 9 notebooks and 4 calculators is Tk. 2688. Find the price of
one calculator?

Solution:
Let the price of one notebook is n
and the price of one calculator = c

ATQ,
6n = 2c
c = 3n ........(1)
And,
⇒ 9n + 4c = 2688
⇒ 9n + 4(3n) = 2688
⇒ 21n = 2688
⇒ n = 2688/21
∴ n = 128

From (1),
∴ c = 3n = 3 × 128 = 384

∴ Price of one calculator c = Tk. 384

Question: p + q : q + r : r + p = 4 : 5 : 6 and p + q + r = 30, find q =?

Solution:
Given that,
p + q : q + r : r + p = 4 : 5 : 6
and p + q + r = 30 ......(1)

Let,
p + q = 4k, q + r = 5k, r + p = 6k

Now,
⇒ p + q + q + r + r + p = 4k + 5k + 6k
⇒ 2(p + q + r) = 15k
⇒ p + q + r = 15k/2
⇒ 15k/2 = 30 [from 1]
⇒ k = 60/15
∴ k = 4

And,
⇒ r + p = 6k
⇒ r + p = 6 × 4
∴ r + p = 24 .....(2)

From (1),
⇒ p + q + r = 30
⇒ q = 30 - (r + p)
⇒ q = 30 - 24
∴ q = 6

Question: What is the value of (255 - 55) ÷ 4 × 15 - 504 ÷ 3 =?

Solution:
(255 - 55) ÷ 4 × 15 - 504 ÷ 3
= 200 ÷ 4 × 15 - 504 ÷ 3
= 50 × 15 - 168
= 750 - 168
= 582

Question: If the sum of two numbers is 22 and their difference is 8. Find the product of these two numbers?

Solution:
Let, two numbers are, a and b
a + b = 22
a - b = 8

We know,
ab = {(a + b)/2}² - {(a - b)/2}²
= {22/2}² - {8/2}²
= (11)² - (4)²
= 121 - 16
= 105
∴ ab = 105

So the product of these two numbers is 105

Question: What will come in the place of the question mark in the following question- 40% of 50% of 3/4 of 2400 = ?

Solution:
40% of 50% of 3/4 of 2400 = ?
⇒ 40% × 50% × (3/4) × 2400 = ?
⇒ (40/100) × (50/100) × 3/4 × 2400 = ?
⇒ (2/5) × (1/2) × (3/4) × 2400 = ?
⇒ (6/40) × 2400 = ?
⇒ ? = 360

∴ The value of ? is 360

Question: Which one of the following is a rational number?

Solution:
We know,
rational + irrational = irrational

√2 × √9
= √2 × 3
= 3√2 [irrational]

√3 × √4
= √3 × 2
= 2√3 [irrational]

√2 × √16
= √2 × 4
= 4√2

√3 × √27
= √3 × 3√3
= (√3)² × 3
= 3 × 3 = 9 [rational number]

Question: A sum of Tk. 1360 has been divided among A, B and C such that A gets 2/3 of what B gets and B gets 1/4 of what C gets. B's share is?

Solution:
Given that,
Total amount = Tk. 1360
A gets 2/3 of what B gets ⇒ A = 2B/3
B gets 1/4 of what C gets ⇒ B = C/4 ⇒ C = 4B

ATQ,
A + B + C = 1360
⇒ (2B/3) + B + 4B = 1360
⇒ (2B + 3B + 12B)/3 = 1360
⇒ 17B/3 = 1360
⇒ B = (1360 × 3)/17
∴ B = 240

∴ B’s share = Tk. 240

Question: If one-sixth of one-third of a number is 10, then what is one-fifth of the number?

Solution:
Let, the number is x,

ATQ,
⇒ (1/6) × (1/3) × x = 10
⇒ x /18 = 10
⇒ x = 10 × 18
∴ x = 180

Now, find one-fifth of the number is,
x/5 = 180/5 = 36

So, one-fifth of the number is 36.