ব্যাংক ডেইলি কুইজ [লং কোর্সের অংশ]

Question: If 30% of 1520 + 40% of 800 = x % of 5000, find the value of x.

Solution:
30% of 1520 + 40% of 800 = x% of 5000
⇒ (30/100) × 1520 + (40/100) × 800 = (x/100) × 5000
⇒ 456 + 320 = 50x
⇒ 50x = 776
⇒ x = 776/50
∴ x = 15.52

Question: The price of a motorbike is 1,50,000. How much do you need to pay if you get a 10% discount?

Solution:
For 10% discount,
Original price 100 paid price 90
∴ Original price 1 paid price 90/100
∴ Original price 150000 paid price (90 × 150000)/100
= 135000

Question: Find the value of 25% of 10% of Tk. 800.

Solution:
25% of 10% of 800
= (25/100) × (10/100) × 800
= 20

Question: The price of a t-shirt is Tk. 50. If you buy more than 3 shirts, you will get 12% discount. How much do you have to pay if you buy 8 shirts?

Solution:
The price of 1 t-shirt 50
∴ The price of 8 t-shirt (50 × 8) 
= 400

If price 100 then have to be paid 88
If price 1 then have to be paid 88/100
If price 400 then have to be paid (88 × 400)/100
= 352

Question: If two values are 20% and 60% of a third value, what percentage is the first value of the second value?

Solution:
Let
The third value x
∴ First value (20x)/100 = x/5
∴ Second value (60x)/100 = 3x/5

Now,
(First Value/Second value) × 100
= (x/5) × (5/3x) × 100
= 33.33%

Question: The price of a computer after discount was Tk. 12000. If the discount was 20%, what was the original sales price?

Solution:
In 20% discount,
Discount price 80 taka when original price 100 taka
∴ Discount price 1 taka when original price 100/80 taka
∴ Discount price 12000 taka when original price (12000 × 100)/80 taka
= 15000 taka 

Question: If the height of Rasel is less by 20% than Maruf, the height of Maruf will be greater than that of Rasel by how many percent?

Solution:
Let the height of Maruf is x and height of Rasel is y.
Then, height of Rasel = x - 20% of x
y = x - (20x)/100
⇒ y = x - x/5
⇒ y = (5x - x)/5
⇒ y  = 4x/5
∴ x = 5y/4

Now,
height of Maruf - height of Rasel
= 5y/4 - y
= (5y - 4y)/4
= y/4

∴ Height of Suresh will be greater than that of Ramesh by = {(y/4)/y} × 100
= (y/4) × (1/y) × 100
= 25%

Question: Monir and Mohin bought the same item. Monir paid Tk 15,000. Mohin got discount and paid Tk. 3,000 less than Monir. How much discount did Mohin get?

Solution:
In Tk. 15000 Mohin get discount Tk. 3000
In Tk. 1 Mohin get discount Tk. (3000/15000)
In Tk. 100 Mohin get discount Tk. (3000 × 100)/15000
= Tk. 20

∴ Mohin get 20% discount.

Question: 1200 boys and 800 girls appeared in an examination. If 60% of the boys and 40% of the girls passed the examination, what is the percentage of candidates who failed in the examination?

Solution:
Number of students failed = 40% of boys (1200) + 60% of girls (800)
= (40 × 1200)/100 + (60 × 800)/100
= 480 + 480
= 960

Total number of students = 1200 + 800 = 2000

∴ Percentage of candidates failed = (960/2000)  × 100
= 48%

Question: You have only Tk. 10000. The price of a TV-set is Tk. 11500. Can you buy the TV if you get 10% discount?

Solution:
In 10% discount,
Original price 100 then discount price 90
Original price 1 then discount price 90/100
Original price 11500 then discount price (90 × 11500)/100
= 10350

The discount price is more than I have.
∴ I can't buy  the TV.

Question: Robin spends 70% of his salary and deposits 15% of his salary in the bank. If he is left with Tk. 1500, what is his monthly salary?

Solution:
Let salary of Robin is Rs. x

As per question;
x - (70 % of x + 15 % of x) = 1500
⇒ x - 85% of x = 1500
⇒ 15% of x = 1500
⇒ (15x)/100= 1500
⇒ x = (1500 × 100)/15
∴ x = 10000

Question: The price of a math book is Tk. 500, but you have only Tk. 350 with you. If you get a discount of 20%, how much money do you need to borrow from a friend so that you can buy the book?

Solution:
In 20% discount,
Original price 100 taka then discount price 80 taka
Original price 1 taka then discount price 80/100 taka
Original price 500 Taka then discount price (80 × 500)/100 Taka
= 400 taka

I need  to borrow = (400 - 350) Taka
= 50 taka

Question: On increasing the price of tickets for a show by 20 % the audience decreases by 30%. What is the effect on revenue?

Solution:
Effect on revenue
= percent increase - percent decrease - (percent increase × percent decrease)/100
= 20 - 30 - (20 × 30)/100
= - 10 - 600/100
= -10 - 6
= - 16 %

'-' sign shows decrease in revenue.

Question: The certain worth of a certain sum due sometime hence is Tk. 1800. If the true discount is Tk. 180, what is the banker's gain?

Solution:
PW = Tk. 1800
TD = Tk. 180

PW (present worth) = FV (face value) - TD (true discount)
⇒ Face value = present worth + true discount
= 1800 + 180
= 1980

True discount is the simple interest on the present value for the unexpired time.
Now, simple interest on Tk. 1800 for unexpired time = Tk. 180
The rate of simple interest = (180/1800) × 100% = 10%

Banker's discount is the simple interest on the face value of the bill for unexpired time.
simple interest on Tk. 1980 for unexpired time or remaining time.
R = 10%
Banker's discount = 1980 × (10/100) = 198

Banker's gain = Banker's discount - True discount
= 198 - 180
= 18

Alternative Solution:
Banker's gain = (True discount)²/Present worth
= (180)²/1800
= 18

Question: If the price of sugar increases by 10%, by what percentage a housewife should reduce the consumption of sugar so that expense is not increased?

Solution:
Let the price be Tk. x per kg
Consumption be y kg

Expenditure = price × consumption
⇒ Expenditure = x × y

Price of sugar is increased by 10%
New price of sugar = Tk. 1.1x per kg

Let new consumption be z kg
New Expenditure = (1.1x) × z

New Expenditure = old Expenditure
⇒ (1.1x) × z = x × y
⇒ z = y/1.1

Reduction in consumption = (y - z) = y - y/1.1 = y/11

Percentage reduction in consumption = (reduction in consumption/original consumption)× 100
Percentage reduction in consumption = [(y/11)/y] × 100 = 100/11 = 9.09% ≈ 9.1%