ব্যাংক মডেল টেস্ট [সাপ্তাহিক]

Question: Mamun invested 77500 tk in CT bank. In two years how much compound interest will he get, if the first year rate of interest was 10% and second year had 2% more than first year?

Solution:
Rate of Interest for Year 1 = 10% 
Rate of Interest for Year 2 = 10 + 2 = 12%

For compound Interest, Total Amount = P {1 + (R/100)}ⁿ
∴ Compound Interest = Amount - Principal = P {1 + (R/100)}ⁿ - P
= 77500{1 + (10/100)}¹ × {1 + (12/100)}¹ - 77500   [1st year 10% and 2nd year 12%]
= 77500[{1 + (10/100)}¹ × {1 + (10/100)}1 - 1]
= 77500 {(11/10) (112/100) - 1}
= 77500{(1232/1000) - 1}
= 77500(232/1000)
= 775(232/10)
= 17980 tk

Question: Six friends are sitting in a circle facing inwards. Priti and Ashwini are exactly opposite to each other. Sachin is in between Priti and Dipen. Dipen is immediately to the left of Ashwini. Rishi is not exactly opposite to Dipen. Who is just right to Ashwini?

Solution:

So, Rishi is just right to Ashwini.

Question: A person has to completely put each of three liquids: 403 litres of petrol, 465 litres of diesel and 496 litres of Mobil Oil in bottles of equal size without mixing any of the above three types of liquids such that each bottle is completely filled. What is the least possible number of bottles required?

Solution: For the least number of bottles, the capacity of each bottle must be maximum.
The capacity of each bottle = HCF of 403 liters, 465 liters, and 496 liters
= 31 liters.

For petrol, required number of bottles = 403/31 = 13
For diesel, required number of bottles = 465/31 = 15
For mobil, required number of bottles = 496/31 = 16

Hence,
required number of bottles = 13 + 15 + 16 = 44

Question: A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:

Solution:

Question: In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples?

Solution:
Number of ways of (selecting at least two couples among five people selected) = ⁵C₂ × ⁶C₁
As remaining person can be any one among three couples left.
∴ Required probability = (⁵C₂ × ⁶C¹)/¹⁰C₅
= (10 × 6)/252
= 60/252
= 5/21

Question: On multiplying a number by 7 all the digit in the product appear as 3's , the smallest such numbers is -

Solution:
Let's check the options one by one:
47649 × 7 = 333543; This result is not all 3's.
47719 × 7 = 333033; This result is not all 3's.
47619 × 7 = 333333; This result is all 3's!
48619 × 7 = 340333; This result is not all 3's.

Question: If θ lies in the first quadrant and cos²θ - sin²θ = 1/2. then the value of tan²2θ + sin²3θ is-

Solution:
cos²θ - sin²θ = 1/2
⇒ cos2θ = 1/2
⇒ cos2θ = cos60°
⇒ 2θ = 60°
⇒ θ = 30°

Now, tan²2θ + sin²3θ
= tan²60° + sin²90°
= 3 + 1
= 4

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