২২৬৪১
Three pipes P, Q and R can fill a tank in 6 hours. After working all three together for 2 hours, R is closed and P and Q can fill the remaining part in 7 hours. The number of hours taken by R alone to fill the tank is-
উত্তর
14
সমাধান
P, Q & R alltogether can fill 1/6 th of the tank in 1 hour
So, in 2 hours they fill = 2×1/6 = 1/3 of the tank
Remining part to be filled = 1 - 1/3 = 2/3 of the tank
P & Q together in 7 hours can fill 2/3 of the tank
So, P & Q together in hour can fill = 2/(3×7) = 2/21 of the tank
So, R alone can fill in 1 hour = 1/6 - 2/21 = (7 - 4)/42 = 1/14 of the tank
Therefore, R alone can fill the tank in 14 hours.
২২৬৪২
Present age of Samad and Akmal are in the ratio of 5:4 respectively. Three years later, the ratio of their ages will become 11:9 respectively. What is Akmals present age?
উত্তর
24
সমাধান
Let their present ages be 5x and 4x respectively.
Three years later,
(5x + 3) : (4x + 3) = 11 : 9
or, (5x + 3) / (4x + 3) = 11/9
or, 9(5x + 3) = 11(4x + 3)
or, 45x + 27 = 44x + 33
or, 45x - 44x = 33 - 27
or, x = 6
So, present age of Akmal = 4x = 4×6 = 24 years
২২৬৪৩
The ratio between the length and breadth of a field is 7:5. The perimeter of the field is 360 meter. What is the area of the field?
উত্তর
7875 sq. meter
সমাধান
Let the length and breadth be 7x and 5x meters respectively.
Then, perimeter, 2(7x + 5x) = 360
or, 2×12x = 360
or, 24x = 360
or, x = 360/24 = 15
Area = length×breadth = 7x × 5x = 35x2 = 35×152 = 35×225 = 7875 m2
২২৬৪৪
Roman covers 17 kilometer in 5 hours. How much time does he need to cover 10.2 kilometer?
উত্তর
3 Hrs
সমাধান
He can cover 17 km in 5 hrs
So, He can cover 10.2 km in 5×10.2/17 hrs = 3 hrs
২২৬৪৫
Arif incurred a loss of 25% by selling a used mobile phone set at taka 1500. How much could he gain/lose by selling that 2200 taka?
উত্তর
10% gain
সমাধান
Let the original price be A.
Then, A - 25% of A = 1500
or, A - 0.25A = 1500
or, 0.75A = 1500
or, A = 1500/0.75 = 2000 TK
Gain = (2200 - 2000)/2000 × 100% = 10%
২২৬৪৬
Rumi and Rony can finish a task, working together, in 12 days. If Rony alone can finish that in 20 days, how many days will Rumi need to finish the task working alone?
উত্তর
30
সমাধান
Together the can finish 1/12 of the work in a day.
Rony alone can finish 1/20 of the work in a day.
Rumi alone can finish = 1/12 - 1/20 = (5 - 3)/60 = 1/30 of the work in a day.
So, Rumi alone can finish the work in 30 days.
২২৬৪৭
The average age of 40 employees in a branch of a bank is 35 years. When a new employee joined the bank the average age increased to 35.5 years. What is the age of the new employee?
উত্তর
55.5
সমাধান
Total age of 40 employees = 40×35 = 1400 years
Total age of 41 employees = 41×35.5 = 1455.5 years
Age of the new employee = 1455.5 - 1400 = 55.5 years
২২৬৪৮
What should be added with 15480 to make it exactly divisible by 14?
উত্তর
6
সমাধান
Here, 15480 ÷ 14 = 1105; remainder = 10
Number to be added = 14 - 10 = 4
২২৬৪৯
If x is an integer then which of the following must be odd?
উত্তর
2x+3
সমাধান
Let, x=2then, 2x+3=2×2+3=7 which is odd
২২৬৫০
A wire that weight 24 kilogram is cut into two pieces so that one of these two pieces weigh 16 kilogram and is 34 meter long. If the weight of each piece is proportional to its length , how long is the other piece?
উত্তর
17 meters
সমাধান
Weight of the other peice = 24 - 16 = 8 kg
Here, weight ∝ length
or, (length/weight)second = (length/weight)first
or, (length/8)second = (34/16)first
So, length of the other peice = 34 / 16 × 8 = 17 meters