ব্যাংক ডেইলি কুইজ [লং কোর্সের অংশ]

Question: In a survey of 400 students, 65% play basketball, 45% play football, and 15% play neither sport. What percent of students play both sports?

Solution:
Let,
x% students play both sports
∴ (65 - x)% + (45 - x)% + x% + 15% = 100%
⇒ 65% + 45% + 15% - x% = 100%
⇒ 125% - x% = 100%
∴ x% = 125% - 100% = 25%

Question: If 10^x equals 0.1 percent of 10^y, where x and y are integers, which of the following must be true?

Solution:
ATQ,
10^x = 0.1% × 10^y
⇒ 10^x = (0.1/100) × 10^y
⇒ 10^x = 0.001 × 10^y
⇒ 10^x = 1 × 10^{y - 3}
⇒ 10^x = 10^{y - 3}
⇒ x = y - 3
∴ y = x + 3

Question: The price of a laptop is 50,000. How much do you need to pay if you get a 15% discount?

Solution:
For 15% discount,
Original price 100 paid price 85
∴ Original price 1 paid price 85/100
∴ Original price 50000 paid price (85 × 50000)/100
= 42500

Question: The price of rice falls by 20%. How much rice can be bought now with the money that was sufficient to buy 20 kg of rice previously?

Solution:
Let
Tk. 100 be spend on rice initially for 20 kg.
As the price falls by 20%, new price for 20 kg rice,
= (100 - 20% of 100)
= 100 - 20 
= 80

New price of rice = 80/20 = 4 

Rice can be bought now = 100/4 = 25kg

Question: A number reduced by 30% becomes 280. What percent should it be increased so that it becomes 500?

Solution:
Let, the number be x

Now, x - 30% of x = 280
⇒ x - (30x/100) = 280
⇒ (100x - 30x)/100 = 280
⇒  70x/100 = 280
⇒ 70x = (280 × 100)
⇒ x = (280 × 100)/70
⇒ x = 400

Required increase = 500 - 400 = 100
∴ Increase % = (100/400) × 100%
= 25%

Question: A batsman scored 86 runs which included 8 boundaries and 3 sixes. What percent of his total score did he make by running between the wickets?

Solution:
Total score of batsman = 86 runs
runs from boundaries = 4 × 8 = 32
runs from sixes = 6 × 3 = 18
∴ Total runs from boundaries and sixes = 32 + 18 = 50 runs
Scores by running between the wickets = 86 - 50 = 36 runs

percentage of his score made by running between wickets = (36/86) × 100% = 41.86%

Question: If 60% of A's income is equal to 75% of B's income, then B's income is equal to x% of A's income. The value of x is :

Solution:
ATQ,
60 × (A/100) = 75 × (B/100)
⇒ 60A = 75B
⇒ 4A = 5B
⇒ B = 4A/5

Again,
B = A × (x/100)
⇒ 4A/5 = A × (x/100)
⇒ 4/5 = x/100
⇒ 5x = 400
⇒ x = 400/5
∴ x = 80

Question: If an item whose marked price is Tk. 1,000 is sold after two successive discounts of 10% and 15%, then find the price at which the item is sold?

Solution:
Marked price is Tk. 1,000

After 10% discount
= 1000 - 10 of 1000
= 1000 - 100
= 900

After 15% discount
= 900 - 15 of 900
= 900 - 135
= 765

Question: The difference between discount of 35% and two successive discount of 20% on a certain bill was 22, the amount of the bill is = ?

Solution:
st discount = 35%
Single equivalent discount of 20% each
= [20 + 20 - {(20 × 20)/100}]%
= 36%

Difference = 36% - 35%
= 1%

Let the amount of the bill Tk. x
∴ (1/100) × x = 22
⇒ x/100 = 22
∴ x = 2200

Question: In a test, minimum passing percentage for girls and boys are 45% and 60% respectively. A boy scored 767 marks and failed by 313 marks. What are the minimum passing marks for girls?

Solution:
Minimum pass percentage for Boys = 60%
Minimum pass percentage for girls = 45%

A boy gets 767 and failed by 313
Passing marks for boys= 767 + 313 = 1080

Now
60% = 1080
1% = 1080/60
45% = (1080 × 45)/60
= 810

Question: 45% of a number is 1350. What is 75% of that number?

Solution:
Let the number be x
Then,
45% of x = 1350
45x/100 = 1350
x = (1350 × 100)/45
x = 3000

75% of 3000 = 3000 × (75/100)
= 2250

Question: The single discount which is equivalent to discount of 10%, 20% and 25% is -

Solution:
Let marked price be 100%.
⇒ S.P = (90/100) × (80/100) × (75/100) × 100
⇒ S.P = 54%

Discount will be 100 – 54 = 46%

∴ The single discount will be 46%

Question: In an election 4% of votes cast are invalid. A candidate gets 55% of casted votes and wins the election by 4800 votes. Find the total number of votes casted.

Solution:
বিজয়ী প্রার্থী ভোট পায়= 55%
বৈধ ভোট = (100 - 4)% = 96%

বিজয়ী প্রার্থী বৈধ ভোটের শতকরা পায় = (55 × 96)/100
= 52.8%

পরাজিত প্রার্থী ভোট পায় = (96 - 52.8)%
= 43.2%

বিজয়ী প্রার্থী ও পরাজিত প্রার্থীর ভোটের পার্থক্য = (52.8 - 43.2)%
= 9.6%

প্রশ্নমতে
9.6% = 4800
1% = 4800/9.6
100% = (4800 × 100)/9.6
= 50000