২২৪২১
A wheel makes 1000 revolutions in covering a distance of 88 km. The diameter of the wheel is -
উত্তর
28m
সমাধান
A distance equal to the circumference of the wheel is covered in each revolution.
So, 1000 x circumference = total distance
or, 1000 x 2πr = 88000 [in meter]
or, 2r = 88000 / (1000 x π )
or, diameter = 28 m
২২৪২২
A 140 liter mixture of milk and water contains 20% water. How much milk , in liter, must be added to the mixture so that the new mixture will contain a water and milk ratio of 1: 7?
উত্তর
84 liter
সমাধান
Amount of water in mixture = 20% of 140 = 20/100 of 140 = 28 liter
Amount of milk in mixture = 140 - 28 = 112 liter
For, new mixture, the amount of water remains the same.
Now, milk : water = 7 : 1
milk / water = 7 / 1
or, milk = 7 x water = 7 x 28 = 196 liter
So, more milk needed = 196 - 112 = 84 liter
২২৪২৩
The average age of 12 students is 20 years. If the age of one more student is included, the average decreases by 1, what is the age of the new student?
উত্তর
7
সমাধান
Total age of 12 students = 12 x 20 = 240 years
New average = 20 - 1 = 19 years
Total age of (12 + 1 = 13) students = 13 x 19 = 247
So, age of the new student = 247 - 240 = 7 years
২২৪২৪
If 120% of x is equaly to 80% y, which of the following is equal to (x +y)?
উত্তর
2.5x
সমাধান
120% of x = 80% of y
or, y = 120/80 of x = 3/2 of x = 3x/2
Now, x + y = x + 3x/2 = 5x/2 = 2.5x
২২৪২৫
A number consists of two digits. The sum of the digits is 9. If 63 is subtracted from the number its digits are interchanged. Find the number.
উত্তর
81
সমাধান
Let X and Y be the digits of decimal and unit places respectively. So, the number is 10X + Y. If 63 is subtracted from the number, it becomes 10Y + X.
Now, X + Y = 9 - - - - - - - (i)
Again, 10X + Y - 63 = 10Y + X
or, 10X - X + Y - 10Y = 63
or, 9X - 9Y = 63
or, X - Y = 63/9
or, X - Y = 7 - - - - - - (ii)
[(i) + (ii)]>> X + Y + X - Y = 9 + 7
or, 2X = 16
or, X = 8
So, 8 + Y = 9
or, Y = 9 - 8 = 1
So, the number is 81.
২২৪২৬
One day at a school , one-twelfth of the students were absent and 20% of those present went on a field trip. If the number of students staying back at school that day was 704 , how many students are enrolled in that school?
উত্তর
960
সমাধান
Let the number of students enrolled at PQR school be x
x/12 students were absent
So, 11x/12 students were present
number of students went on a field trip = 11x/12 * 1/5 = 11x/60
Number of students who were absent or went on a field trip = x/12 + 11x/60 = 16x/60 = 4x/15
Number of students staying in the school = x - 4x/15 = 11x/15
ATQ,
11x/15 = 704
∴x = 960
ans: 960
২২৪২৭
For the final step in a calculation , chunnu accidentally accidentally divided by 1,000 instead of multiplying by 1,000. what should he do to his incorrect answer to correct it?
উত্তর
Multiply by 1,000,000
সমাধান
at first he should multiply by 1000 to undo his mistake, then multiply by 1000 again.
When you multiply by 1000 twice, that’s the same as multiplying by (1000 × 1000) = 1,000,000
ans: 1,000,000
২২৪২৮
The lengths of the sides of triangle T are x +1 , 2x, and 3x. The sum of the degree measures of the three interior angles of T is--
উত্তর
180
২২৪২৯
If the average of 5, 9 ,M and n is 12 m what is the average of (m +7) and (n -3)?
উত্তর
19
সমাধান
here,5+9+m+n4=12=> m + n = 34 …………(i)and,Av of (m+7) and (n-3) = (m+7)+(n-3)2=m+n+42=34+42 ………………….. [m+n=34]= 19
২২৪৩০
The length of a rectangular field F is 3 km greater than the side of a square field M , and the width of field F is 3 km less then the side of field M. If the area of field M is m2 square km, what is the area of field F?
উত্তর
m2 +9
সমাধান
Side of field M = √m2 = m km
Length of field F = (m + 3) km
Width of field F = (m - 3) km
So, area of field F = Length x Width = (m + 3) x (m - 3) = m2 - 9