২২২১১
A motorcycle costs Tk. 2500 when it is brand new. At the end of each year it is worth 4/5 of what it was at the beginning of the year. What is the motorcycle worth when it is 3 years old?
উত্তর
Tk. 1280
সমাধান
At the end of first year, the motorcycle is worth = 4/5 of 2500 = 2000 TK
At the end of second year, the motorcycle is worth = 4/5 of 2000 = 1600 TK
At the end of third year, the motorcycle is worth = 4/5 of 1600 = 1280 TK
[Shortcut = 4/5 x 4/5 x 4/5 x 2500]
২২২১২
The average of 20, 70 and x is 40. If the average of 20, 70, x and y is 50, then y =?
উত্তর
80
সমাধান
Here, 20 + 70 + x = 3 x 40 = 120
Now, 20 + 70 + x + y = 4 x 50
or, y = 200 - (20 + 70 + x)
or, y = 200 - 120
So, y = 80
২২২১৩
If X and Y are prime numbers, then which of the following cannot be the the sum of X and Y?
উত্তর
23
সমাধান
Here, the highest total is 23.
Now, Prime numbers upto 23 = 2, 3, 5, 7, 11, 13, 17, 19, 23.
Here, 2 + 3 = 5; 2 + 11 = 13; 5 + 11 = 16;
But, no pair of numbers from these numbers adds up to 23.
২২২১৪
If Tk. 4,500 was invested in a share when the price per share was Tk. 9 and Tk. 3,000 was invested in another share when the price per share was Tk. 10. What was the average price per share purchased?
উত্তর
Tk. 9.375
সমাধান
When tk 9, number of share = 4500/9 = 500
When tk 10, number of share = 3000/10 = 300
Average price = Total price of share / Total number of share = (4500 + 3000) / (500 + 300) = 7500/800 = 9.375
২২২১৫
It costs X taka each to make the first thousand copies of a CD and Y taka to make each subsequent copy. How many taka will it cost to make Z copies (Z is greater than 1000) of the CD?
উত্তর
1000(X-Y) +YZ
সমাধান
For first thousand copies = 1000X tk
As, Z is greater than 1000, we have to substract 1000Y from 1000X.
And for extra copies, the cost = YZ
So, the equation = (1000X - 1000Y) + YZ = 1000(X - Y) + YZ
২২২১৬
In a mixture of 30 liters, the ratio of acid and water is 7: 3. How much more water is to be added to get a new mixture containing acid and water in the ratio of 3: 7?
উত্তর
40 liters
সমাধান
Let the amount of water needed be W.
Initialy, the mixture contains (7 / (7 + 3) x 30 = 21 liter of acid and 30 - 21 = 9 liter of water.
Now, 21 : (9 + W) = 3 : 7
or, 21 / (9 + W) = 3 / 7
or, 3(9 + W) = 21 x 7
or, 27 + 3W = 147
or, 3W = 147 - 27
or, W = 120/3 = 40 liter
২২২১৭
A container is 1/2 full., When 8 gallons is removed the container is 1/10 full. What is the capacity of the container in gallon?
উত্তর
20
সমাধান
Let n be the total capacity of the container.
ATQ,
n/2 - 8 = n/10
or,n/2 - n/10 = 8
or, 4n = 80
or, n = 20 liters
so, 20 liters need to be added to make it full
২২২১৮
Find the number that should be placed in the gap of the series: 80, 96, -, 128
উত্তর
112
সমাধান
80 + 16 = 96
96 + 16 = 112
112 + 16 = 128
২২২১৯
The length of the train that takes 8 second to pass a pole when it runs at a speed of 3 km/hr is-
উত্তর
80m
সমাধান
***The question is erroneous. If the speed is 36 km/hr then the solution is as follows:
36 km/hr = 36 x 1000 /3600 m/s = 10 m/s
So, the length of the train = 10 x 8 = 80 m.
২২২২০
A man travels 5 miles towards west, 2 miles towards south, then again 5 miles towards west. What is the direct distance of destination from the starting point?
উত্তর
12 miles
সমাধান
***The question is erroneous.
The man is 5 + 5 = 10 miles westward an 2 miles southward from his starting point. So, considering a right - angled triangle, his direct distance from the initial point will be (102 + 22)1/2 ≈ 10.2 miles.