২৩২৩১
X and Y invested in a business. They earned some profit which they divided in the ratio of 2: 3. If X invested Tk. 40,000 the amount invested by Y is:
উত্তর
Tk. 60,000
সমাধান
Hints: x/y = 2/3 = 4000o/?
? = 40000 × 3 /2 = 60000(ans)
২৩২৩২
If 5 men and 9 women can do a piece of work in 19 days, then in how many days will 3 men and 6 women do the same work?
উত্তর
15
সমাধান
Hints: short method
Time = Men1 × women1 × Time1 / Men1 × women2 + Men2 × women1
= 5 × 9 × 19/ 5 × 6 + 9 × 3 = 15
২৩২৩৩
A person travels form P to Q at a speed of 40 kmph and returns by increasing his speed by 50%. What is the average speed for both the trips?
উত্তর
50 kmph
সমাধান
let, P to Q is x km. Thus he travels 2x km
1st Speed = 40kmph and 2nd speed will be = 40 + 40X50% = 60kmph
Now, time to go P to Q = x/40 and time to come from Q to P is = x/60 and total time taken = x/40 + x/60 = 5x/120 = x/24
Thus, Average speed = 2x/(x/24) = (24X2x)/x = 48kmph
Ans: Average Speed 48km/h
২৩২৩৪
A train 360 m long is running at a speed of 45 km/hour. In what time will it pass a bridge 140 m long?
উত্তর
40 seconds
সমাধান
Hints: train অতিক্রম করে নিজের length এবং bridge এর length 45km/hr = ( 45÷3.6)ms - 1 = 12.5 ms - 1
Time = 140 + 360 /12.5 = 40seconds.
২৩২৩৫
A man wishes to cover his floor with tiles, each one measuring 3/4 inch by 2 inches. If his room is rectangular, measuring 12 feet by 18 feet, how many such tiles will he need?
উত্তর
20736
সমাধান
Area of each tiles = 34×2 = 32 sq· inch = 12×18 sq·inch = 216 sq·inch∴216×14432 = 20736 ∵feet = 12 inch
২৩২৩৬
The speed of a boat in still water is 10 km/hr. If it can travel 26 km downstream and 14 km upstream in the same time, the speed of the stream is:
উত্তর
3 km/hr
সমাধান
Hints: ধরি, stream এর speed x km/hr
এখন, উভয়ক্ষেত্রে একই সময় লাগে,
সময় = দূরুত্ব /বেগ
26 /(10 + x) = 14/(10 - x)
260 - 26x = 140 + 14x
40x = 120
x = 3 km/hr
২৩২৩৭
Johan walks 10 miles at an average rate of 2 miles per hour and returns on a bicycle at an average rate of 10 miles per hour. How long does the entire trip take him?
উত্তর
6 hours
সমাধান
We know, v = st∴t = sv∴Time to go = 102 = 5 hourand time to return = 101 = 1 hour∴Total time = 5 + 1 = 6 hour
২৩২৩৮
A sum of money amounts to Tk. 9800 after 5 years and Tk. 12005 after 8 years at the same rate of simple interest per annual is:
উত্তর
12%
সমাধান
Hints: 8 বছর এবং 5 বছর এর মাঝের 3 বছরের interest = ( 12005 - 9800) = 2205
Simple interest 5 বছরের জন্য = ( 2205/3 × 5) = 3675
Principle = (9800 - 3675) = 6125
Rate = {(100 × 3675)/(6125 × 5)}% = 12%
২৩২৩৯
In theis diagram AB=AC angle A = 40 degree and BD is perpendicular to AC at D. how many degrees are there in angle DBC?
উত্তর
20 degree
সমাধান
△ABC এ AB = AC,∠B = ∠C∴∠A + ∠B + ∠C = 180∘⇒∠B + ∠C = 180∘ - 40∘⇒∠B + ∠C = 140∘⇒2∠B = 140∘∴∠B = 70∘ = ∠CAgain, △ABD এ ∠ADB = 90∘∠A = 40∘∴∠DBA = 180∘ - 90∘ - 40∘ = 50∘
∴∠DBC = ∠ABC - ∠DBA = 70∘ - 50∘ = 20∘
২৩২৪০
Consider the following series: 3,4,6,9,13,............. What comes next?
উত্তর
18
সমাধান
vacillate মানে ইতস্ততঃ করা
determined মানে দৃঢ়প্রতিজ্ঞ
তাই এরা opposite.