২০৮২১
If the compound interest on a sum for 2 years at 12.5% per annum is TK. 510 the simple interest on the same at the same rate for the same period of time is:
উত্তর
TK. 480
সমাধান
Ler, capital is P tk
In compound interest c = p( 1 + r)n
So, interest = p (1 + r) n - p
According to question,
p + (1 + r)n - p = 510
p( 1 + 12.5/100) 2 - p = 510
p ( 1.125)2 - p = 510
p { (1.125)2 - 1} = 510
p = 510/0.2656 = 1920.18 tk
Again, Simple interest,
I = pnr = 1920.18 ×2×0.125 = 480 tk
২০৮২২
১, ৯, ২৫, ৪৯, ৮১......... ধারাটির পরবর্তী সংখ্যাটি কত?
উত্তর
121
সমাধান
প্রদত্ত ধারা গুলো বিজোড় সংখ্যর বর্গ
১২ = ১
৩২ = ৯
৫২ = ২৫
৭২ = ৪৯
৯২ = ৮১
১১২ = ১২১ [ এটা পরবর্তী সংখ্য ]
২০৮২৩
Sixty-five percent of a number is 21 less than four-fifth of that number. What is the number?
উত্তর
140
সমাধান
Let, the number x
According to question,
x × 65 /100 + 21 = 4x/5
65x/100 - 4x/5 = - 21
( 65x - 80x)/100 = - 21
- 15x = - 2100
x = 140
২০৮২৪
An article when sold at a gain of 5% yields TK. 15 more than when sold at a loss of 5%. Its cost price would be:
উত্তর
TK. 150
সমাধান
At, 5% gain, selling price = 105 Tk.
Again, 5% loss, then selling price = 95tk
Difference of both price = ( 105 - 95) tk = 10 tk
Selling price 10 tk more than cost price = 100 tk
selling price 15 tk more than cost price ( 100×15)/10 = 150 tk.
২০৮২৫
An express train travelled at an average speed of 100 km/hr, slopping for 3 minutes after every 75 km. How long did it take to reach its destination 600 km from the starting point?
উত্তর
6 hrs 21 min
সমাধান
The train travels 100 km in 1 hr
the train travels 1 km in 1/100 hr
the train travels 75 km in ( 75×1)/100 = (75×60)/100 = 45 minutes
To travel 600 km it takes 600/75 = 8 steps
On its way it stop in 7 steps
On its way it stop waste ( 3×7) mints = 21 steps
So total time = (45×8) + 21 minta = (360 + 21) mints = 6 hr 21 mints
২০৮২৬
If 18 pumps can raise 2170 tonnes of water in 10 days , working 7 hours a day; in how many days will 16 pumps raise 1736 tonnes of water , working 9 hours a day?
উত্তর
7
সমাধান
18 pumps can rise 2170 tonnes in 7 hour in 10 days
18 pumps can rise 2170 tonnes in 1 hour in ( 10×7) days.
1 pumps can rise 1 tonnes in 1 hour in ( 10×7×18)/2170 days
16 pumps can rise 1736 tonnes b8n 9 hour in ( 10×7×18×1736)/ ( 2170×16×9) = 7 days
২০৮২৭
To fill a tank , 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is educed to two-fifth of its present?
উত্তর
62.5
সমাধান
Let, capacity of the bucket is x litter
So, the capacity of tank is 25x litrer
Reduced capacity of bucket is 25x/5 litrer
So, to fill tank bucket requires = 25x/(2x/5) = (25x × 5) / 2x = 62.5 bucket
২০৮২৮
যদি a+b = 2, ab = 1 হয়, তবে a এবং b এর মান যথাক্রমে-
উত্তর
1, 1
সমাধান
দেওয়া আছে,
a + b = 2 .......(1)
এবং ab = 1 .......(2)
আমরা জানি,
(a - b)2 = (a + b)2 - 4ab
= > (a - b)2 = 22 - 4.1
= > (a - b)2 = 4 - 4
a - b = 0 ..........(3)
(1) + (3) হতে পাই,
2a = 2
= > a = 1
(1) - (3) হতে পাই,
2a = 2
= > b = 1
a = 1 এবং b = 1.
২০৮২৯
A man can do a piece of work in 5 days. But with the help of his son, he can do it in 3 days. In what time can the son do it alone?
উত্তর
7.5 days
সমাধান
Man can do in 1 days = 1/5 portion
Man + son can do in 1 days = 1/3 portion
Man can do alone in 1 days = ( 1/3 - 1/5) portion = 2/15 portion
2/15 portion can be done in 1 days
1 (hole) can be done in = 15/2 days = 7.5 days
২০৮৩০
একটি নৌকা স্রোতের অনুকুলে ঘন্টায় ৮ কি.মি এবং স্রোতের প্রতিকূলে ৪ কি.মি যায়। নৌকার বেগ কত?
উত্তর
৬ কিমি
সমাধান
নৌকা + স্রোত = ৮
নৌকা - স্রোত = ৪
- - - - - - - - - - - - - - - - - - -
২ x নৌকা = ১২
বা, নৌকা = ৬ কি.মি./ঘণ্টা