ব্যাংক ডেইলি কুইজ [লং কোর্সের অংশ]

Question: A Teacher distributes x chocolate among 30 students but 3 students absent. For this every one get one chocolate extra. Find the value of x?

Solution:
Given that,
Total students = 30
Absent students = 3
Chocolates distributed = x

Now,
Each student initially gets = x/30
Each student after 3 absent = x/27
Difference between both = 1

ATQ,
(x/27) − (x/30) = 1
⇒ x{(30 − 27)/810} = 1
⇒ x(3/810) = 1
⇒ x = 810/3
∴ x = 270

∴ The value of x = 270 chocolates

Question: On simplification √{(0.65)² - (0.16)²} reduces to-

Solution:
Given that,
√{(0.65)² - (0.16)²}
Since, a² - b² = (a - b)( a + b)
= √{(0.65 + 0.16)(0.65 - 0.16)}
= √{(0.81)(0.49)}
= √{(0.9)(0.9)×(0.7)(0.7)}
= 0.9 × 0.7
= 0.63

Question: Two positive numbers are in the ratio 3 : 2. The product of their HCF and LCM is 3456. Find the sum of both the numbers.

Solution:
Let two numbers are 3a and 2a.

HCF × LCM = 1st no. × 2nd no.
⇒ 3456 = 3a × 2a
⇒ 3456 = 6a²
⇒ a² = 576
∴ a = 24 

∴ Sum of both the numbers = 3a + 2a = 5a = 5 × 24 = 120

Question: Solve: (81.84 + 118.16) ÷ 5³ = 1.2 × 2 + ?

Solution:
Given that,
(81.84 + 118.16) ÷ 5³ = 1.2 × 2 + ?
⇒ 200 ÷ 5³ = 1.2 × 2 + ?
⇒ 200 ÷ 125 = 1.2 × 2 +?
⇒ 1.6 = 2.4 + ?
∴ ? = - 0.8

Question: If 35% of a certain number is 49, then find the number-

Solution:
Let the number be x.
Then,
⇒ 35% of x = 49
⇒ (35/100) × x = 49
⇒ 7x/20 = 49
⇒ x = (20 × 49)/7
∴ x = 140

Question: If x + y = 21 and xy = 110, find the value of x² + y² = ?

Solution:
Given that,
x + y = 21 and xy = 110

We know that,
(x + y)² = x² + y² + 2xy
⇒ x² + y² = (x + y)² - 2xy
⇒ x² + y² = 21² - 2 × 110
⇒ x² + y² = 441 - 220
∴ x² + y² = 221

Question: The sum of 7 consecutive natural numbers is 77. Find how many of these are prime numbers?

Solution:
Given that,
The sum of seven consecutive natural numbers = 77

Now,
Let the numbers be n, n + 1, n + 2, n + 3, n + 4, n + 5, n + 6 respectively
∴ 7n + 21 = 77
⇒ 7n = 77 - 21
⇒ 7n = 56
⇒ n = 56/7
∴ n = 8

So the numbers is 8, 9, 10, 11, 12, 13, 14
Out of these 11, 13 are prime numbers

∴ Required prime numbers is 2

Question: If X + Y = 174, and X is half of Y, then find the value of X.

Solution:
Given that,
X + Y = 174 …… (i)
Y = 2X …… (ii)
On solving (i) and (ii), we get,
⇒ X + 2X = 174
⇒ 3X = 174
⇒ X = 174/3
∴ X = 58

Question: The difference between the average of all prime numbers between 30 and 60 and the average of all prime numbers between 15 and 30 is-

Solution:
The prime numbers between 30 and 60 are 31, 37, 41, 43, 47, 53 and 59.

∴ The average of all prime numbers between 30 and 60 is,
= (31 + 37 + 41 + 43 + 47 + 53 + 59)/7
= 311/7
= 44.43

And,
The prime numbers between 15 and 30 are 17, 19, 23 and 29.

∴ The average of all prime numbers between 15 and 30 is,
= (17 + 19 + 23 + 29)/4
= 88/4
= 22

∴ Required difference = (44.43) - 22 = 22.4

Question: The sum of all the factors of 100 is-

Solution:
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100

∴ the sum of these number is,
1 + 2 + 4 + 5 + 10 + 20 + 25 + 50 + 100
= 217

So the sum of all factors of 100 is 217.

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: Find the value of x, if (x/7) - (x/9) = 2

Solution:
Given that,
(x/7) - (x/9) = 2
⇒ (9x - 7x)/63 = 2
⇒ 2x = 2 × 63
∴ x = 63

Question: What will come in the place of the question mark in the following question- 40% of 50% of 3/4 of 1800 = ?

Solution:
40% of 50% of 3/4 of 1800 = ?
⇒ 40% × 50% × (3/4) × 1800 = ?
⇒ (40/100) × (50/100) × 3/4 × 1800 = ?
⇒ (2/5) × (1/2) × (3/4) × 1800 = ?
⇒ (6/40) × 1800 = ?
⇒ ? = 270

∴ The question mark is replaced by 270