ব্যাংক ডেইলি কুইজ [লং কোর্সের অংশ]

Question: The ratio of three numbers is 3 : 4 : 5 and the sum of their squares is 5000. The sum of the numbers is-

Solution:
Let, the number be 3x, 4x, 5x

According to the question,
(3x)² + (4x)² + (5x)² = 5000
⇒ 9x² + 16x² + 25x² = 5000
⇒ 50x² = 5000
⇒ x² = 5000/50
⇒ x² = 100
∴ x = 10

∴ The sum of the numbers = 3x + 4x + 5x
= 30 + 40 + 50
= 120

Question: A and B invest in business in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share in Tk. 1710, the total profit is:

Solution:
Let the total profit be Tk. 100.
After paying to charity, A's share = (95 × 3/5) = 57

If A's share is Tk. 57, total profit = 100.
If A's share is Tk. 855, total profit = (100/57 × 1710)
= Tk. 3,000

Question: If Tk. 1564 be divided into three parts, proportional to 1/2 : 2/3 : 3/4, then the first part is:

Solution:
Given ratio = 1/2 : 2/3 : 3/4
= 6 : 8 : 9

The first part = 1564 × (6/23)
= 408

Question: Masud and Akram invested in a business and gained a profit which was divided in the ratio of 2 : 3. If Masud invested Tk. 80000, then what was the amount invested by Akram?

Solution:
Given ratio = 2 : 3
Let,
Masud invested 2x Taka
Akram invested 3x Taka

ATQ,
2x = 80000
∴ x = 40000

∴ Akram invested 3x Taka = 3 × 40000 Taka
= 120000 Taka

Question: In a certain zoo, the ratio of tigers to zebras to giraffes in stock is 3 : 5 : 7. If there are 96 zebras and giraffes total in stock, how many tigers are there?

Solution:
5x + 7x = 96
⇒ 12x = 96
⇒ x = 96/12 = 8

number of tigers = 3x
= 3 × 8
= 24

Question: If 6 × P's capital = 8 × Q's capital = 10 × R's capital, find the ratio of their capitals?

Solution:
Let,
6 × P's capital = 8 × Q's capital = 10 × R's capital = x
Now,
P's capital = x/6
Q's capital = x/8
R's capital = x/10

∴ Ratio of capitals of P, Q, R = x/6 : x/8 : x/10
= 20 : 15 : 12

Question: The ages of Sabit and Sumit are in the ratio of 7 : 3 respectively. After 6 years, the ratio of their ages will be 5 : 3. What is the sum of their ages?

Solution:
Let, their ages are 7x, 3x

ATQ,
(7x + 6)/(3x + 6) = 5/3
⇒ 3(7x + 6) = 5(3x + 6)
⇒ 21x + 18 = 15x + 30
⇒ 21x - 15x = 30 - 18
⇒ 6x = 12
∴ x = 2

The difference in their ages is = 7x + 3x
= 10x
= 10 × 2
= 20 years

Question: A, B, and C started a business by investing Tk.150000, Tk.120000, and Tk.135000 respectively. Find the share of B out of the annual profit of Tk. 56700?

Solution:
Ratio of the investments of A, B and C = 150000 : 120000 : 135000
= 150 : 120 : 135
= 10 : 8 : 9
Sum of the ratio = 10 + 8 + 9
= 27

∴ B's share = 56700 × (8/27)
= 16,800 Tk.

Question: If p : q = 3 : 2, find ratio (4p + 5q) : (4p - 5q).

Solution:
(4p + 5q) : (4p - 5q)
= q(4p/q + 5) : q(4p/q - 5)
= (4 × 3/2 + 5) : (4 × 3/2 - 5)
= (6 + 5) : (6 - 5)
= 11 : 1

Question: A sum of Tk. 427 is to be divided among A, B and C in such a way that 3 times A’s share, 4 times B’s share and 7 times C’s share are all equal. The share of C is?

Solution:
Given total sum = Tk. 427
And given that 3 times A’s share, 4 times B’s share and 7 times C’s share are all equal.
Or, 3A = 4B = 7C

But given,
A + B + C = 427

Now, expressing A and B in terms of C,
(7C/3) + (7C/4) + C = 427
∴ C = 84

Question: An office opens at 9 a.m. and closes at 5.30 p.m. with a lunch break of 17 minutes. What is the ratio of lunch breaks to the total period in the office?

Solution:
The ratio of lunch breaks to the total period in the office = 17/{(8 × 60) + 30}
= 17/510
= 1/30
= 1 : 30

Question: Anis's and Bulbul's shares in a business are in the ratio of 5 : 3. If Anis has invested Tk. 70000 for 12 months, for what period Bulbul has invested Tk. 60000?

Solution:
Let,
Bulbul has invested for x months
Anis : Bulbul = (70000 × 12) : (60000 × x) = 5 : 3
⇒ 84 : 6x = 5 : 3
⇒ 14 : x = 5 : 3
⇒ 14/x = 5/3
⇒ 5x = 42
⇒ x = 42/5
∴ x = 8.4

Question: Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:

Solution:
Let the third number be x

Then, first number = 120% of x = 120x/100 = 6x/5
Second number = 150% of x = 150x/100 = 3x/2

∴ Ratio of first two numbers = 6x/5 : 3x/2
= 12x : 15x
= 4 : 5

Question: Abir, Babul, and Chandan invest 63000, 56000, and 84000 respectively to start a business. After one year, the profit is distributed in the ratio of their investments. If Chandan's share of profit is Tk. 54000, find the total profit earned.

Solution:
Let the total profit = x
The ratio of investment = 63000 : 56000 : 84000
= 63 : 56 : 84
= 9 : 8 : 12
Now, sum of the ratios = 29

Chandan's share = (12/29) × x = 54000
⇒ x = (54000 × 29)/12
x = 130500

Hence, the total profit = Tk. 130500

Question: If (3/2)P = (5/7)Q = (6/5)R, then what is P : Q : R?

Solution:
(3/2)P = (5/7)Q = (6/5)R .................(1)

LCM of their numerators = LCM of (3, 5, 6) = 30

Divide the eq. (1) by 30.
3P/(2 × 30) =5Q/(7 × 30) = 6R/(5 × 30)
⇒ P/20 = Q/42 = R/25

∴ P : Q : R = 20 : 42 : 25