ব্যাংক ডেইলি কুইজ [লং কোর্সের অংশ]

Question: The ratio of the number of sides of a square to the number of edges of a cube is 

Solution: 
the number of sides of a square = 4
the number of edges of a cube = 12

∴ The ratio of the number of sides of a square to the number of edges of a cube is = 4 : 12
= 1 : 3

Question: The Mathematics textbook for Class VII has 320 pages. The chapter ‘Symmetry’ runs from page 261 to page 272. The ratio of the number of pages of this chapter to the total number of pages of the book is

Solution: 
The chapter ‘Symmetry’ runs for pages = 272 - 261 + 1
= 12

The ratio of the number of pages of this chapter to the total number of pages of the book is = 12 : 320
= 3 : 80

Question: Rahim and Karim started a business investing Tk. 26000 and Tk. 30000 respectively. Out of a total profit of Tk. 7000, Rahim's share is -

Solution:
Given,
Investment ratio = 26000 : 30000
= 13 : 15
Sum of the ratio's = 13 + 15 = 28

∴ Rahim's share = 7000 × (13/28)
= Tk. 3250

Question: In a box, the ratio of red marbles to blue marbles is 7 : 4. Which of the following could be the total number of marbles in the box?

Solution: 
18, 19, 21 কোনটিই 7 + 4 বা 11 দ্বারা নি:শেষে বিভাজ্য নয়। 
অতএব, সঠিক উত্তর 22

Question: On a shelf, books with green cover and that with brown cover are in the ratio 2 : 3. If there are 18 books with green cover, then the number of books with brown cover is

Solution: 
Green cover books 2x
Brown cover books 3x

2x = 18 
⇒ x = 18/2 = 9

Brown cover books = 3 × 9 
= 27

Question: Labib started a business with Tk. 2100 and is joined afterward by Shishir with Tk. 3600. After how many months did Shishir join if the profits at the end of the year are divided equally?

Solution:
Suppose,
Shishir joined after x months.

Then,
2100 × 12 = 3600 × (12 - x)
⇒ 252 = 432 - 36x
⇒ 36x = 180
∴ x = 5

∴ Shishir joined after 5 months

Question: If a bus travels 160 km in 4 hours and a train travels 320 km in 5 hours at uniform speeds, then the ratio of the distances traveled by them in one hour is 

Solution: 
Distance traveled by bus in one hour= 160 / 4 
= 40 

Distance traveled by bus in one hour= 320 / 5
= 64

Ratio = 40 : 64
= 5 : 8 

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

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

Question: The ratio between the sale price and the cost price of an article is 7 : 6. What is the ratio between the profit and the cost price of that article?

Solution: 
Let C.P. = 6x and S.P. = 7x
Then, gain = x.
∴ Required ratio = x : 6x = 1 : 6

Question: An office opens at 9 a.m. and closes at 5.30 p.m. with a lunch break of 30 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 = 30/{(8 × 60) + 30}
= 30/510
= 1/17