২২৩৫১
The food stock in a cantonment having 1200 soldiers is enough to last for 30 days after 10 days another 300 new soldiers joined the same cantonment. For many more days will the remaining food stock last?
উত্তর
20
সমাধান
Remaining days = 30 - 10 = 20 days
For 1200 soldiers, the stock will last for 20 more days
For 1 soldier, the stock will last for 20 x 1200 more days
So, for (1200 + 300 = 1500) soldiers, the stock will last = 20 x 1200 / 1500 = 16 more days
২২৩৫২
The population of a town exceeds one-fifth of its own population by 5000. What is the population of the town?
উত্তর
6,250
২২৩৫৩
By selling an article, Shila earned a profit equal to 1/4 th of the price she bought it for. If she sod it at TK.375, what was the cost price?
উত্তর
TK. 300
সমাধান
Let the cost price be P.
Now, Cost price + Profit = Selling price
or, P + P/4 = 0.375
or, 5P/4 = 0.375
or, P = 0.375 x 4 / 5 = 0.300 TK
২২৩৫৪
If x =2y +3 and y= -2 , then
উত্তর
x =-1
সমাধান
Here, x = 2y + 3
or, x = 2 ( - 2) + 3 [y = - 2]
or, x = - 4 + 3
So, x = - 1
২২৩৫৫
The average age of three persons is 30 years. If the ratio of three ages is 3: 5: 7, what is the age of the youngest person?
উত্তর
18 years
সমাধান
Total age of them = 30 x 3 = 90 years.
Sum of the ratios = 3 + 5 + 7 = 15
So, the age of the youngest person = 3 / 15 x 90 = 18 years
২২৩৫৬
X purchased some pens for TK. 120. If the price per piece of pen was TK. 3 less, he would have received 2 more pens. How many pens did he purchase?
উত্তর
8
সমাধান
Let the number of pens be N.
Then, price of each pen = 120/N
He would get (N + 2) pens if the price of each pen was [120/N - 3].
So, 120 / (N + 2) = (120/N) - 3
or, 120 / (N + 2) = (120 - 3N) / N
or, 120N = (120 - 3N) (N + 2)
or, 120N = 120N + 120 x 2 - 3N2 - 3N x 2
or, 3N2 + 6N + 120N - 120N - 240 = 0
or, 3N2 + 6N - 240 = 0
or, N2 + 2N - 80 = 0
or, N2 + 10N - 8N - 80 = 0
or, N(N + 10) - 8(N + 10) = 0
or, (N + 10) (N - 8) = 0
or, N - 8 = 0 [N + 10 = / 0]
So, N = 8
২২৩৫৭
If your body mass on the surface of the earth is 42 kg, what would be your body mass on the surface of the moon?
উত্তর
42 kg
সমাধান
Mass of object is independent of gravity. Therefore, it will be the same everywhere.
২২৩৫৮
Sumi walks to her office at the rate of 4 miles per hour. If she increases her walking speed by 1 mile per hour , she would reach her office half an hour earlier than the previous time. What is the distance in miles of her office from her house?
উত্তর
10
সমাধান
Let the distance and time be d mile and T hours respectively.
So, d = 4T.
Again, d = (4 + 1) (T - 1/2)
or, 4T = 5(T - 1/2)
or, 4T = 5T - 5/2
or, 5T - 4T = 5/2
or, T = 5/2 hours
So, d = 4T = 4 x 5/2 = 10 mile.
২২৩৫৯
Given AB = 4, AC = 5, the perimeter of the rectangle is -
উত্তর
14
সমাধান
AB2 + BC2 = AC2
or, BC2 = AC2 - AB2
or, BC = √(AC2 - AB2)
or, BC = √(52 - 42) = 3
So, perimeter of the rectangle = 2(AB + BC) = 2(4 + 3) = 14
২২৩৬০
The share price of a bank decreased by 5% on the 15th of November, but increased by 10% of the next day. What was the overall rate of loss or gain?
উত্তর
4.58% gain
সমাধান
Let the initial share price be S.
Decreased share price = S - 5% of S = 0.95S
Increased share price = 0.95S + 10% of 0.95S = 1.045S
So, gain percentage = (1.045S - S) / S x 100% = 4.5%