২২৩১১
The average of a, b, c is 6 and a-b = 4, ab = 21, what is the value of c?
উত্তর
8
সমাধান
Here, a - b = 4
or, a = b + 4 - - - - - - (i)
Again, ab = 21
or, (b + 4)b = 21 [from (i)]
or, b2 + 4b - 21 = 0
or. b2 + 7b - 3b - 21 = 0
or, b(b + 7) - 3(b + 7) = 0
or, (b + 7) (b - 3) = 0
or, b - 3 = 0 [b ≠ - 7]
So, b = 3.
Now, a + b + c = 6 x 3
or, a + b + c = 18
or, b + 4 + b + c = 18 [from(i)]
or, 3 + 4 + 3 + c = 18
or, c = 18 - 10 = 8
২২৩১২
A man can row a boat at 10 km/hr in still water. If the speed of the stream is 6 km/hr, the time taken to row a distance of 80 km downstream is:
উত্তর
20 hours
সমাধান
Relative downstream speed = 10 + 6 = 16 km/hr
So, time needed = distance / speed = 80 / 16 = 5 hours.
২২৩১৩
A truck dirver must complete a 180-mile trip in 4 housr. If his average speed is 50 miles per hour for first 3 hours , then how fast must he travel for the final hour?
উত্তর
30
সমাধান
Distance travelled in the first 3 hours = 50 x 3 = 150 mile.
Remaining distance to be covered in the final hour = 180 - 150 = 30 mile
২২৩১৪
From 7 boys and 5 girls, 6 are to be selected for admission for a particular course. In how many ways can this be done if there must be exactly 3 girls?
উত্তর
350
সমাধান
Ways of selecting 3 girls out of 5 = 5C3 = 10
Number of boys to be selected = 6 - 3 = 3
Ways of selecting 3 boys out of 7 = 7C3 = 35
So, total ways = 10 x 35 = 350
২২৩১৫
If 15 men can reap a field in 35 days, in how many days will 21 men reap the field?
উত্তর
25 days
সমাধান
15 men can reap the field in 35 days
1 man can reap the field in 35 x 15 days
So, 21 men can reap the field in 35 x 15 / 21 = 25 days
২২৩১৬
The ratio of the angles of a triangle is 2: 3: 4. What is the largest angle in degrees?
উত্তর
80
সমাধান
Let the angles be 2x, 3x and 4x respectively.
Now, 2x + 3x + 4x = 180°
or, 9x = 180°
or, x = 180/9 = 20
So, the largest angle = 4x = 4 x 20 = 80°
২২৩১৭
A man can row downstream at 10 kmph and upstream at 5 kmph. The man's rowing rate in still water is ----
উত্তর
7.5 km/hr
সমাধান
Let the man's rowing rate and stream's flowing rate be U and V respectively.
So, U + V = 10
And, U - V = 5
- - - - - - - - - - - - - - - - - - - - - - -
U + U = 10 + 5 [By addition]
or, 2U = 15
So, U = 7.5 km/hr
২২৩১৮
A Company employs 15 persons, each works 44 hours a week. If 4 persons are absent, how many hours a week would the rest of the persons have to work to make up the time lost?
উত্তর
60
সমাধান
Total work hours per week = 44 x 15 = 660
Persons present = 15 - 4 = 11
Working hour per person = 660 / 11 = 60 hours per week.
২২৩১৯
A manufacturer of jam wants to make a profit of Tk. 0.65 each to make first 100 jars of jams and Tk. 0.55 to make each jar after the first 100. How much profit he will make from 300 jars of jam?
উত্তর
Tk. 175
সমাধান
Profit from first 100 jars = 0.65×100 = 65 TK.
Profit from the rest (300 - 100 = 200) jars = 0.55×200 = 110 TK
Total profit = 65 + 110 = 175 TK
২২৩২০
If the circumference of a circle is increased by 50%, its area will be increased by:
উত্তর
125%
সমাধান
Circumference of a circle increases only with radius. Therefore, radius of the circle gets increased by 50%. Now, new radius = R + 50% of R = 1.5R
Initial area = π R2
New area = π (1.5R)2 = 2.25 π R2
Percent increase = ((2.25 π R2) - (π R2)} / (π R2) x 100% = 125%