২২৫৮১
what is the total interest on Tk. 800 at 12.5 % per annum for 9 months in taka?
উত্তর
75
সমাধান
Interest, I = P n r
Here, P = 800 TK, n = 9/12 year, r = 12.5/100 = 1/8
So, I = 800 × 9/12 × 1/8 = 75 TK
২২৫৮২
In a two digit number, if it is known that its unit's digit exceeds its ten's digit by 2 and that product of the given number and the sum of its digits is equal to 144, then the number is-
উত্তর
24
সমাধান
Let the ten's digit be x
Then, unit's digit = x + 2
Number = 10x + (x + 2) = 11x + 2
Sum of digits = x + (x + 2) = 2x + 2
∴ (11x + 2)(2x + 2) = 144
⇒ 22x2 + 26x - 140 = 0
⇒ 11x2 + 13x - 70 = 0
⇒ 11x2 + (35 - 22)x - 70 = 0
⇒ 11x2 + 35x - 22x - 70 = 0
⇒ (x - 2)(11x + 35) = 0
⇒ x = 2
Hence, required number = 11x + 2 = 24 (ans)
২২৫৮৩
Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is -
উত্তর
48
সমাধান
Relative speed = (60 + 90) km/hr = 150 km/hr = 150×1000/3600 m/s = 41.67 m/s
Total distance = (1.1 + 0.9) km = 2 km = 2000 m
Time taken to cross each other = 2000/41.67 ≈ 48 seconds
২২৫৮৪
If 'n' is a natural number, then (6n2+6n) is always divisible by-
উত্তর
6 only
সমাধান
Here, 6n2 + 6n = 6(n2 + n) which is always divisible by 6.
২২৫৮৫
Nazir can wash his car 15 minutes while his son takes twice as long. If they work together how many minutes will the job take them?
উত্তর
10
সমাধান
His son can wash the car in (15 × 2 = 30) minutes
Nazir can wash 1/15 part of the car in 1 minute
His son can wash 1/30 part of the can in 1 minute
Together they can wash (1/15 + 1/30 = 1/10) part of the car in 1 minute
So, together they can wash the whole car in 10 minutes.
২২৫৮৬
In a 500 m race the ratio of the speeds of two contestants Ajmal and Badal is 3:4. If Ajmal has a head start of 140 km then Ajmal wins by-
উত্তর
60m
সমাধান
To reach the winning post Ajmal will have to cover a distance of (500 - 140)m = 360 m.
While Ajmal covers 3 m, Badal covers 4 m.
While Ajmal covers 360 m, Badal covers (4/3×360)m = 480 m.
Thus, when Ajmal reaches the winning post, Badal covers 480 m and therefore remains 20 m behind.
∴ Ajmal wins by 20 m. (ans)
২২৫৮৭
A batsman in his 17th innings makes a score of 85 and thereby increases his average by 3, his average after the 17th innings is:
উত্তর
37
সমাধান
Let the average of the first 16 innings be A.
Total of the 16 innings = 16A
New average = A + 3
New total of 17 innings, 17(A + 3) = 16A + 85
or, 17A + 51 = 16A + 85
or, 17A - 16A = 85 - 51
or, A = 34
So, new average after 17th innings = A + 3 = 34 + 3 = 37
২২৫৮৮
Income of A is 25% less than B. How much percent B's income would be more than that of A?
উত্তর
33.5%
সমাধান
Let their income be A and B respectively.
Now, A = B - 25% of B = B - B/4 = 3B/4
or, B = 4A/3
Now, B - A = 4A/3 - A = A/3 = A/3 × 100% = 33.33% of A
২২৫৮৯
Two pipes A & B would fill a tank in 20 & 30 minutes respectively. Both pipes being open, find when A must be turned off so that tank may be just filled in 15 minutes.
উত্তর
After 10 minutes
সমাধান
Let the time be T minutes after which pipe A need to turned off. Both of the pipes remain open together only for T minutes.
Pipe A fills 1/20 of the tank in 1 minute.
Pipe B fills 1/30 of the tank in 1 minute
Together in 1 minute they fill (1/20 + 1/30 = 1/12) of the tank.
Together in T minutes they fill = T/12 of the tank
In (15 - T) minutes, pipe B alone can fill = (15 - T)/30 of the tank
Now, T/12 + (15 - T)/30 = 1
or, {15T + 6(15 - T)}/180 = 1
or, (15T + 90 - 6T) / 180 = 1
or, 9T = 180 - 90
or, 9T = 90
So, T = 10 minutes
২২৫৯০
What percentage of profit is made by selling an article at a certain price if by selling at two third of that price there would be a loss of 20%?
উত্তর
20%
সমাধান
Let the cost price and sell price be A and S respectively.
ATQ, (A - 2S/3) /A = 20/100
or, (A - 2S/3) / A = 1/5
or, (A - 2S/3) = A/5
or, 2S/3 = A - A/5
or, 2S/3 = 4A/5
or, S = 4A/5 × 3/2
or, S = 6A/5
Now, profit = (S - A) / A × 100%
= (6A/5 - A) / A × 100%
= (A/5) / A × 100%
= 20%