ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

Question: If each child is given 10 sweets, there are 3 sweets left over. But if each is given 11, then the number of sweets is 4 less. Find the number of sweets.

Solution:
Let, the number of children be x.

ATQ,
10x + 3 = 11x - 4
⇒ 11x - 10x = 4 + 3
∴ x = 7

So, number of sweets = (10 × 7) + 3 = 73

Question: Find the least multiple of 23. which when divided by 18, 21 and 24 leaves remainders 7, 10 and 13 respectively.

Solution:
Here, (18 - 7) = 11, (21 - 10) = 11 and (24 - 13) = 11
L.C.M of 18, 21 and 24 is 504.

Let, the required number be 504x - 11.
Least value of x for which (504x - 11) is divisible by 23 is x = 6

Required number = (504 × 6) - 11 = 3024 - 11 = 3013.

Question: Two-fifth of one-fourth of three seventh of a number is 15. What is the half of the number?

Solution: 
Let the number is a

ATQ,
a × (3/7) × (1/4) × (2/5) = 15
⇒ 3a/70 = 15
a = 350 

∴ Half of the number is = 350/2 = 175

Question: The sum of three consecutive odd natural numbers each divisible by 3 is 63. What is the smallest among them?

Solution: 
let, the numbers 3x, 3x + 6, 3x + 12

ATQ,
3x + 3x + 6 + 3x + 12 = 63
⇒ 9x + 18 = 63 
⇒ 9x = 45
∴ x = 5

The smallest among them is = 3 × 5 
= 15

Question: A number is 2/5 times of another number. If the sum of two numbers is 98, what is the difference of the two numbers?

Solution:
Let, a number is x
another number is 2x/5

ATQ,
x + 2x/5 = 98
⇒ (5x + 2x)/5 = 98
⇒ 7x/5 = 98
⇒ 7x = 98 × 5
⇒ 7x = 490
∴ x = 70

So, a number is 70
another number is 2x/5 = (2 × 70)/5 = 28
∴ Difference = 70 - 28
= 42

Question: The L.C.M of two numbers is 12 times their H.C.F. The sum of H.C.F and L.C.M is 403. If one number is 93, find the other.

Solution:
Let, H.C.F of the numbers be x and L.C.M be 12x.

ATQ,
x + 12x = 403
⇒ 13x = 403
⇒ x = 403/13
∴ x = 31

So, H.C.F = 31 and L.C.M = 12 × 31 = 372

Other number = (31 × 372)/93 = 124

Question: Two numbers are in the ratio 5 : 2. If the difference of their squares is 84, then find the largest number-

Solution: 
দুটি সংখ্যার অনুপাত ৫ : ২
সংখ্যা দুটি ৫x, ২x

প্রশ্নমতে,
(৫x)^২ - (২x)^২ = ৮৪
⇒ ২৫x^২ - ৪x^২ = ৮৪
⇒ ২১x^২ = ৮৪ 
⇒ x^২ = ৪
∴ x = ২

সংখ্যা দুটি ১০, ৪ 
বড় সংখ্যাটি ১০

Question: Find the smallest number of five digits exactly divisible by 16, 24, 36, and 54.

Solution:
The smallest number of five digits is = 10000
The number must be divisible by the LCM of 16, 24, 36, and 54 = 432
On dividing 10000 by 432, we get 64 as the remainder.

So, required number is = 10000 + (432 - 64)
= 10000 + 368
= 10368

Question: A waiter's income consists of his salary and tips. During one week his tips were 5/4 of his salary. What fraction of his income came from tips?

Solution:
Let, salary = Tk. x
Then, tips = Tk. 5x/4

Total income = x + (5x/4)
= 9x/4

∴ Required fraction = (5x/4) × (4/9x) = 5/9

Question: The simplified value of
 

Solution:

Question: A certain number of horses and an equal number of men are going somewhere. Half of the owners are on their horses back while the remaining ones are walking along leading their horses. If the number of legs walking on the ground is 70. Then how many horses are there?

Solution: 
Let, the number of horses be x. 
Then, the number of men = x
Number of man walking = x/2

ATQ,
4x + (x/2) . 2 = 70
⇒ 5x = 70
∴ x = 14

Question: The difference between a number and its two-fifths is 510. What is the ten percent of that number?

Solution:
Let, the number be x.

ATQ,
x - (2x/5) = 510
⇒ (5x - 2x)/5 = 510
⇒ 3x/5 = 510
⇒ 3x = 510 × 5
⇒ x = 2550/3
∴ x = 850

∴ সংখ্যাটির 10% = 850 × 10/100 = 85 

Question: The L.C.M of 1/3, 5/6, 2/9, 4/27 is?

Solution:
L.C.M of 1, 5, 2, 4 is 20
H.C.F of 3, 6, 9, 27 is 3

We know,
Required L.C.M = L.C.M of 1, 5, 2, 4/H.C.F of 3, 6, 9, 27
= 20/3

Question: What will be the least number that when doubled will be exactly divisible by 12, 18, 21 and 30?

Solution:
12 = 2 × 2 × 3
18 = 2 × 3 × 3
21 = 3 × 7
30 = 2 × 3 × 5

L.C.M. of 12, 18, 21 30 = 2 × 3 × 2 × 3 × 7 × 5 = 1260
Required number = 1260/2 = 630

Question: The L.C.M. of two numbers is 48. The numbers are in the ratio 2 : 3. Then the sum of the numbers is: 

Solution: 

Question: 7 is added to a certain number; the sum is multiplied by 5, the product is divided by 9 and 3 is subtracted from the quotient. The remainder left is 12. The number is:

Solution:
Let the original number be x

Now
{5(x + 7)/9} - 3 = 12
⇒ {5(x + 7) - 27}/9 = 12
⇒ 5(x + 7) - 27 = 108
⇒ 5x + 35 - 27 = 108
⇒ 5x + 8 = 108
⇒ 5x = 100
∴ x = 20