ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

Question: Two friends, Akash & Beenu had some candies each. One of them had 15 candies more than the other. The candies with Akash was 60% of the total candies with them. How many candies did each have?

Solution:
Let the candies with be (x + 15) and x.
Therefore, x + 15 = (60/100) × (x + 15 + x)
⇒ (x + 15) = (3/5)(2x + 15)
⇒ 5x + 75 = 6x + 45
∴ x = 30

So, the candies of two friends are 45 and 30.

Question: A cloth merchant bought 35 shirts, each at a price of Tk. 280. He sold each of them for Tk. 308. Find his percentage profit.

Solution:
The profit percentage remains same for one unit as well for all the units. Thus the calculations should be done for one unit only.
CP = Tk. 280
SP = Tk. 308
Profit = 308 - 280 = 28.

Profit percentage = (28/280) × 100 = 10%

Question: A refrigerator is on sale for 20% off the original price. A store-wide sale results in an additional reduction of 25%. What is the total discount based on the original price?

Solution:
Let
 x = original price.

First discount: 
x(1 - 0.20)
= 0.80x (sale price).

Second discount: 
0.80x(1 - 0.25)
= 0.60x (final sale price)

Therefore, the final price is 60% of the original price.
∴  the total discount = 1 - 0.60 = 0.40 
∴ % total discount = 40%

Question: A fruit seller had some oranges. He sells 30% oranges and still has 140 oranges. Originally, he had-

Solution:
Suppose originally he had x oranges.
Then,
(100 - 30)% of x = 140.
⇒ (70/100) × x = 140
⇒ x = (140 × 100)/70 = 200

Question: An article is sold for Tk. 2400 at a profit of 25%. What would have been the actual profit or loss if it had been sold at Tk. 1800?

Solution:
Firstly let us find the cost price of the same. C.P. = 2400 × (100/125) = 1920.
New selling price = 1800
Loss = 1920 - 1800 = 120
∴ Loss percentage = 100 × (120/1920) = 6.25%.

Question: Taposh purchased an mp3 player, originally priced at Tk. 2900, but discounted by Tk. 270. What percent discount did Taposh receive on the mp3 player?

Solution:
percent discount = (270/2900) × 100%
= 9.31%

Question: What percentage of numbers from 1 to 30 has 1 or 9 in the unit's digit?

Solution:
Such numbers from 1 to 30 are 1, 9, 11, 19, 21, 29
Number of such numbers =6
Required percentage is (6/30) × 100% = 20%

Question: A retail fruit vendor buys pineapples at a score for Tk. 200, and retails them at a dozen for Tk. 156. What % was his gain or loss?

Solution:
C.P of 1 pineapple = 220/score = 200/20 = 10 [Note: 1 score = 20 nos.]
S.P of 1 pineapple = 156/dozen = 156/12 = 13.
∴ Profit = 13 - 10 = 3
∴ % Profit = 100 × (3/10) = 30%

Question: A restaurant owner allows employees to purchase meals for 28% off list price. An employee purchases a meal with a list price of Tk. 16.50.  What does she pay for the meal?

Solution:
If she gets a 28% discount, she pays 72% of the list price:

∴ Amount to be paid = (72/100) × 16.50
= 11.88

Question: In ABC College, 65% of students are less than 20 years of age. The number of students more than 20 years of age is 2/3 of number of students of 20 years of age which is 42. What is the total number of students in the ABC College?

Solution:
Let total number of students is x.
Then, number of students more than or equal to 20 years of age = (100 - 65)% of x = 35% of x.
As per the question,
35% of x = 42 + (2/3 of 42)
⇒ 35x/100 = 70.
⇒ x = (70 × 100)/35
∴ x = 200

Question: Profit obtained by selling a watch at Tk. 320 is equal to 7/5th of the profit obtained by selling the same watch at Tk. 300. What is the cost price of the watch?

Solution:
Let the cost of a watch be x
∴ (320 - x) = (7/5) × (300 - x).
⇒1600 - 5x = 2100 - 7x
⇒ 2x = 500
⇒ x = 250

Question: The banker's gain of a certain sum due 2 years hence at 10% per annum is Tk. 26. Find the present worth.

Solution:
Banker Gain = 26
True Discount = (Bnakers gain × 100)/(rate × time) = (26 × 100)/(10 × 2) =  130

Banker's Gain = Banker's Discount - True discount
⇒ 26 = Banker's discount - 130
∴ Banker's discount = 130 + 26 = 156

Now, banker's discount is the interest on the face value
Let the face value = x
So,
x × (10/100) × 2 = 156
⇒ x × 0.1 × 2 = 156
⇒ x = 156/0.2 = 780

Now,
Present Worth = Face value - True discount
= 780 - 130
= 650

Question: A student erroneously multiplied a number by 2/5 instead of 5/2.What is the percentage error in the calculation?

Solution:
Let the number be 100.
2/5 of 100 is 40 while 5/2 of 100 is 250.
Now the difference is 210 on a base of 250.
Therefore, percentage difference is (210/250) × 100 = 84%.

Question: Mehedi purchased two articles at the same price and sold one at a profit of 20% and the other at a profit of 22.5%. If the difference between the two selling price is Tk. 150, what is the cost price of each of the articles?

Solution:
Let the cost price of each of the articles = 100.
The selling price of the first watch = 120
and the selling price of the second watch = 122.5
The difference in the selling price = 122.5 - 120 = 2.5

The difference in the selling price = 2.5 if the cost price = 100
If the difference in selling price = 150, then the cost price = (150 × 100)/2.5 = 6000

Question: A clothing store offers a dress initially at Tk. 1000. Then one week later, the store offers the dress at 15% off. The dress still doesn't sell, so after another week, the store reduces its new price by 20%. How much does the dress cost now?

Solution:
For the first discount,
we have 1000(1 - 0.15) = 1000(0.85) = 850
So the dress is worth Tk. 850

After the second discount,
we have 850(1 - 0.20) = 850(0.8) = 680

So the final dress price is Tk. 680

Question: Three candidates, Salman, Parimal & Maruf contested an election and received 1800, 3300 and votes 3900 respectively. What percent of the total votes did Salman get?

Solution:
Total no. of votes polled = (1800 + 3300 + 3900) = 9000.
Required percentage = (1800/9000) × 100% = 20%.

Question: A merchant buys 30 kg of rice at Tk. 40/kg, and another 20 kg of rice at Tk. 30/kg. He mixes them and sells half of the mixture at Tk. 36/kg. At what price should he sell the remaining mixture to get an overall profit of 30%?

Solution:
Total cost for the entire quantity of rice = (30 × 40) + (20 × 30) = 1200 + 600 = 1800
If his profit is 30%, then the sales realization = (130/100) × 1800 = 2340.
Total rice = 30 + 20 = 50 kg
He sells 25 kg at Tk. 36/kg = 900.

Therefore to make the said amount of profit, he should sell the remaining 25 kg of rice at 2340 - 900 = 1440

Question: Trader A offers a discount of 25% on the marked price for cash purchase. Trader B offers a trade discount of 20% and a cash discount of 5% on the same article marked at the same price as that of Trader A. As a buyer whom should I buy from if I am to pay cash?

Solution:
Trader A:
If the marked price = 100
then the net price to the buyer = 0.75 × 100 = 75.

Trader B:
If the marked price = 100,
then the price after 1st discount = 0.8 × 100 = 80 and
the cash price = 0.95 × 80 = 0.76

Since the discount is higher or the price to me as a buyer is lower with Trader A, I should choose to buy from Trader A.

Question: The total population of a village increased from 18000 to 22500 in a decade. The average percentage increase of population per year of that village is-

Solution:
Population increase in 10 years = (22500 - 18000) = 4500.
Increase% of ten year = (4500/18000) × 100% = 25%
∴ Required average = (25/10)% = 2.5%

Question: Three-eighth of 320 chairs was sold at a profit of Tk. 50 each and the rest for Tk. 33600. If the seller makes a profit of 20% on the whole transaction, what is the cost price of each of the chair?

Solution:
Three-eighth of 320 = (320 × 3)/8 = 120

120 chairs were sold at a profit of Tk. 50 each.
Profit on these 120 chairs = 6000.

S.P. of all 320 chairs = (C.P. of 120 chairs + Profit on 120 chairs) + S.P. of 200 chairs
= (120 × C.P) + 6000 + 33600
= (120 × C.P.) + 39600

But these 320 chairs were sold at a profit of 20%.
∴ S. P. of 320 chair is = (120/100) ×(320 × C.P.) = 1.2 × 320 × C.P. = 384 × C.P.

Now,
384 × C.P = 120 × C. P. + 39600
⇒ 384 C.P. = 120 C.P. + 39600
⇒ 264 C.P. = 39600
⇒ C. P. = 150.

Question: A package tour operator allows a 25% discount on his advertised price and then makes a profit of 20%. What is the advertised price on which he gains Tk. 60?

Solution:
Let,
the advertised price = x

Profit = Selling price - Cost Price = 60.
Selling price = 1.2 (C.P.) 
∴  1.2 C.P - C.P. = 60
⇒ 0.2 C.P. = 60
⇒ C.P. = 300
and Selling price = 360.

75% of x = 360
⇒ (75/100)x = 360
⇒ x = (360 × 100)/75
∴ x = 480

Question: A Stationery seller had some Pens, Sharpeners, Erasers & Pencils. He sells 65% of the total units and still has 175 units. Originally, he had-

Solution:
Suppose originally he had x units.
Then,
(100 - 65)% of x = 175.
⇒ (35/100) × x = 175
⇒ x = (175 × 100)/35
∴ x = 500

Question: A shopkeeper sells his goods at a profit of 10%. If he had purchased it at 20% less and sells it at Tk. 10 more, he had a gain of 40%. Find the cost price of the goods.

Solution:
Let the C.P of an article is 100.
ATQ,
S.P will be 110 ..............(1)
If he has purchased it at 20% less, the new C.P = 100 - 20= 80

If the C.P is 80, then he earns a profit of 40% and sells the article at Tk. 10 more than the previous price.
So, when he earns 40% on the new C.P then the profit = (40/100) × 80 = 32

That means if the C.P = 80, the S.P = 80 + 32 = 112 ............(2)

Compare equation 1 and 2, and we get,
The difference between S.P is = 2
But ATQ, it should be 10, i.e., multiple of 5
So, we need to multiply the actual value with 5 then we get actual cost price.
Hence, the C.P of the article is = 100 × 5 = 500

Question: Normally a Play Station costs Tk. 5000, but you only want to pay Tk. 4500. How much discount (in percent) do you want?

Solution:
Discount = 5000 - 4500 = 500

% Discount = (500/5000) × 100 = 10%

Question: The price of a product is reduced by 25%, but the daily sale of the article is increased by 30%. Find the net effect on the daily sale.

Solution:
We can say that,
Total Sale = the price of one unit × no. of units sold

Let
the initial price of product = 100, sale =100 items.
Then, Total Sale = 100 × 100 = 10000

ATQ,
price reduces to 25%.
So, the new price = 100 - 25 = 75
Sale increase to 30%,
So, the new sale = 100 + 30 = 130
Now, the new total sale = 75 × 130 = 9750

Difference = 10000 - 9750 = 250
% net effect = (diff/original)× 100
= (250/10000) × 100 = 2.5
So, the net effect on daily sale = 2.5% decrease