Bank Math Master

Question: 15% of 40% of a number is 120. What is 24% of that number? 

Solution:
let, a number is x 

x × 0.15 × 0.4 = 120 
⇒ x = 120/( 0.15 × 0.4) 
= 2000 

 24% of that number is = 2000 × 0.24 
= 480 

Question: If Anil’s income is 50% less than that of Borhan, then Borhan’s income is what percent more than that of Anil?

Solution: 
Borhan's income:
= {50/(100 - 50) × 100 }%
= 100%
Borhan's income is 100% more than that of Anil's

Question: By selling a shirt for Tk. 300, a shopkeeper gains 20%. During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is-

Solution: 
Marked price = Tk. 300
C.P = (100/120) × 300 =  Tk. 250 

Sale price = 90% of Tk. 300
= 300 × (90/100)
= Tk. 270

Required gain% = {(20/250) × 100}% = 8%

Question: 40% of 265 + 35% of 180 = 50% of ? 

Solution: 
40% of 265 + 35% of 180 = 50% of x
⇒ (265 × 40)/100 + (35 × 180)/100 = x/2 
⇒ 106 + 63 = x/2
⇒ 169 = x/2
∴ x = 338 

Question: A company makes a profit of 5% on its first TK. 1000 of sales each day, and 4% on all sales in excess of 1000 for that day. What would be the profit of the company in a day when sales are TK. 6000?

Solution:
Profit for first TK. 1000 =  1000 × (5/100) = TK. 50

Total sales excess of Tk. 1000 = (6000 - 1000) = Tk. 5000

∴ Profit for excess of Tk. 1000 = 5000 × (4/100) = Tk. 200

∴ Total Profit (50+ 200) = Tk. 250

Question: Three-fourths of a number is equal to 60% of another number and the difference between these two number is 10. What is the sum of these two numbers? 

Solution: 
Let the numbers be x and x + 10

Then, 
3x/4 = 60% of (x + 10)
⇒ 3x/4 = 60(x + 10)/100
⇒ 3x/4 = 3(x + 10)/5
⇒ x/4 = (x + 10)/5
⇒ 5x = 4x + 40
⇒ 5x - 4x = 40 
⇒ x = 40 

The sum of these two numbers = x + x + 10 
= 2x + 10
= 2 × 40 + 10
= 80 + 10 
= 90

Question: A train 175 m long crosses a bridge which is 125 m long in 1 min 40 seconds. What is the speed of the train?

Solution: 
মোট অতিক্রান্ত দূরত্ব = ১৭৫ + ১২৫ মিটার 
= ৩০০ মিটার 

সময় = ১ মিনিট ৪০ সেকেন্ড 
= ৬০ + ৪০ সেকেন্ড 
= ১০০ সেকেন্ড 

বেগ = ৩০০/১০০ মিটার/সেকেন্ড
= ৩ মিটার/সেকেন্ড 

Question: The MRP of a Jacket is given as Tk. 2000 and the merchant decides to provide successive discounts of 30% and 20% on the product. Find the selling price.

Solution: 
After 30% discount, = 2000 - 2000 × 30/100 
= 2000 - 600 
= 1400 

After 20% discount, = 1400 - 1400 × 20/100 
= 1400 - 280 
= 1120 taka 

Question: 800 grams of sugar solution has 30% sugar in it. How much sugar should be added to make 50% in the solution?

Solution:
Amount of sugar = 800 × 30/100
= 240 grams

Let, x gm sugar to be added
ATQ,
(240 + x)/(800 + x) = 50%
⇒ (240 + x)/(800 + x) =  = 1/2
⇒ 480 + 2x = 800 + x
⇒ 2x - x = 800 - 480 
∴ x = 320 gm

Question: 500 sweets were distributed equally among children in such a way that the number of sweets received by each child is 20% of the total number of children. How many sweets did each child receive? 

Solution: 
Let Children = X
A/Q,
500/X = 20% of X
⇒ 500/X = X/5 
⇒ X² =5 × 500 
⇒ X² = 2500
X = 50 

So each children receive = 500/50
= 10

Question: Tea worth Tk. 126 per kg and Tk. 135 per kg are mixed with a third variety in the ratio 1 : 2 : 2. If the mixture is worth Tk. 153 per kg, the price of the third variety per kg will be:

Solution: 
Let, price of third variety x tk per kg 
126y + 135 × 2y + x × 2y = 153 (y + 2y + 2y)
⇒ 126 + 270 + 2x = 765
⇒ 2x = 369
∴ x = 184.5 tk

Question: Akash took a loan from a bank at the rate of 12 % p.a. simple interest. After three years he had to pay Tk. 5400 interest only for the period. The principal amount borrowed by him was:

Solution: 
Let, The principal amount borrowed by him was P 

P × (12/100) × 3 = 5400 
⇒ P = (5400 × 100)/36
= 15000 taka 

Question: Simon rowing against the current can go 2 km per hour. If the speed of the current is 3 km per hour, how much time will he take to cover 32 km, rowing along the current?

Solution: 
ধরি, সায়মনের বেগ x কিমি/ঘণ্টা 
স্রোতের বেগ ৩ কিমি/ঘণ্টা

সায়মন স্রোতের বিপরীতে ২ কিমি/ঘণ্টা বেগে যায়।

x - ৩ = ২
∴ x = ৫ কিমি/ঘণ্টা 

স্রোতের অনুকূলে বেগ = ৩ + ৫ কিমি/ঘণ্টা 
= ৮ কিমি/ঘণ্টা 

স্রোতের অনুকূলে যেতে সময় লাগে = ৩২/৮ ঘণ্টা 
= ৪ ঘন্টা

Question: In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was:

Solution: 
Number of valid votes = 80% of 7500
= 6000

Valid votes polled by other candidate = 45% of 6000
= (45/100) x 6000
= 2700

Question: An amount of Tk. 625 becomes Tk 1296 in 2 years if the interest is compounded half-yearly. What is the rate of compound interest? 

solution:
let the rate be R%

Then,
625 {1 + R/(2 × 100)} ^{2 × 2} = 1296
⇒ (1 + R/200)⁴ = 1296/625
⇒ (1 + R/200)⁴ = (6/5)⁴
⇒ (1 + R/200) = 6/5
⇒ R/200 = 1/5
⇒ R = 40
∴ R = 40%

Question: A train 110 m long is running at the speed of 60 km/hr. In what time will it pass a man who is running at the speed of 6 km/hr in the opposite direction in which the train is moving?

Solution: 
Relative speed = 60 km/hr + 6 km/hr
= 66 km/hr
= 66 ×1000/3600 m/sec 
= 66 × 5/18 m/sec
= 55/3 m/sec

Time needed = 110 /55/3 sec
= 110 × 3/55 sec 
= 6 sec

Question: A motorboat in still water travels at speed of 26 kmph. It goes 42 km upstream in 1 hour 45 minutes. The time taken by it to cover the same distance down the stream will be:

Solution:
মোটরযানের বেগ ২৬ কিমি/ঘণ্টা 

স্রোতের বিপরীতে ১ঘণ্টা ৪৫ মিনিট বা ৭/৪ ঘণ্টায় যায় ৪২ কিমি 
১ ঘণ্টায় যায়  ৪২/৭/৪ কিমি
= ২৪ কিমি 
স্রোতের বেগ = ২৬ - ২৪ কিমি/ঘণ্টা 
= ২ কিমি/ঘণ্টা 

স্রোতের অনুকূলে বেগ = ২৬ +২
= ২৮ কিমি/ঘণ্টা 

৪২ কিমি যেতে সময় লাগে ৪২/২৮
= ৩/২
= ১.৫ ঘণ্টা
= ১ ঘণ্টা ৩০ মিনিট 

Question: There is a dishonest shopkeeper whose claim is that he sells a certain product at a cost of Tk 23/kg, which actually costs him Tk 25/kg. The shopkeeper says that he is taking the loss to let his customers get a better deal. When examined thoroughly, a policeman finds that the shopkeeper is actually using an 800 gms weight in place of a 1 kg weight. How much does he gain or lose?

Solution: 
selling price of 0.8 kg = 23 taka

selling price of 1 kg = 23/0.8 taka 
= 115/4 taka
= 28.75 taka 

percentage profit = {(28.75 - 25)/25} × 100%
= (3.75/25) × 100%
= 15% 

Question: Pritom travels a distance of 9 km from his house to the school by auto-rickshaw at 18 km/hr and returns on rickshaw at 15 km/hr. Find the average speed for the whole journey.

Solution: 
total distance = 9 + 9 = 18 km

time taken by auto rickshaw = 9/18 hr
= 1/2 hr 

time taken by auto rickshaw = 9/15 hr
= 3/5 hr 

total time = 1/2 hr  +  3/5 hr 
= 11/10 hr

average speed = 18/11/10
= 180/11 km/hr
= 16.3 km/hr

Question: In a certain zoo, the ratio of tigers to lions to snakes in stock is 3 : 5 : 7. If there are 48 lions and snakes total in stock, how many tigers are there?

Solution: 
5x + 7x = 48 
⇒ 12x = 48 
⇒ x = 48/12 = 4 

number of tigers = 3x 
 = 3 × 4
= 12