২২৮৮১
If 4 is subtracted from one-fourth of a number, the result is 20. Which of the following is the number.
উত্তর
96
সমাধান
Let the number be X.
ATQ, X/4 - 4 = 20
or, X/4 = 20 + 4
or, X = 24 x 4 = 96
২২৮৮২
The sum of 6 consecutive odd numbers exceeds twice the largest by 38. Find the sum of the six numbers.
উত্তর
72
সমাধান
Let x represent the smallest number. Then the other number are
x + 2, x + 4, x + 6, x + 8 and x + 10. x + 10 is the largest.
The sum of these is 6x + (2 + 4 + 6 + 8 + 10) = 6x + 30
We are told that this is 38 greater than twice the largest, so
6x + 30 = 2(x + 10) + 38 = 2x + 58.
or, 4x = 28
∴x = 7
Then the sum is 6×7 + 30 = 72.
২২৮৮৩
Points A, B, X, and Y are on a straight line, but not necessarily in that order. Given the lengths AB=12, BX=2, and XY=8, what is the length AY?
উত্তর
cannot be determined
২২৮৮৪
The difference between two numbers is 7 and their product is 60, then one of the two numbers must be ---
উত্তর
5
সমাধান
x - y = 7; x = (y + 7)
xy = 60
or , (y + 7).y = 60
or, y² + 7y - 60 = 0
or, (y + 12) (y – 5) = 0
So, Y = - 12,5
So, the two number is 12 and 5
২২৮৮৫
Six workers can do 9 identical jobs in 3 days. How long will it take 4 workers to do 10 such jobs?
উত্তর
5 days
সমাধান
If 6 workers can complete 9 jobs in 3 days, then
6 workers can complete 9/3 = 3 jobs in 3/3 = 1 day, then
6/6 = 1 worker can complete 3/6 = 1/2 job in 1 day, then
4 × 1 = 4 workers can complete 4 × 1/2 = 2 jobs in 1 day, then
4 workers can complete 5 × 2 = 10 jobs in 5 × 1 = 5 days.
২২৮৮৬
A cake is divided into 18 pieces. If Rehana takes 1/3 of the cake and Rahim takes 1/3 of the rest that are left, how may pieces are still left?
উত্তর
8
সমাধান
rehana took = 1/3 of 18 pieces = 6 pieces
ramaining = 12 pieces
rahim took 1/3 of 12 pieces = 4 pieces
total remaining = 12 - 4 = 8 pieces
২২৮৮৭
B and C are points on the straight line AD, on which AB=BC=CD. What percent of AC is AD?
উত্তর
150%
সমাধান
Here, AB + BC + CD = AD
or, AB + AB + AB = AD
or, 3AB = AD
Again, AB + BC = AC
or, AB + AB = AC
or, 2AB = AC
Now, AD/AC = 3AB/(2AB)
or, AD = 3/2×100% of AC = 150% of AC
২২৮৮৮
If the average of two numbers is M, and the larger number is L, what is the other number?
উত্তর
2M-L
সমাধান
average of two numbers is M
one number is L
let second number be X
average = L + X/2
= > M = L + X/2
= > 2M = L + X
= > 2M - L = X
therefore,second number is 2M - L
২২৮৮৯
A mixture of 17 parts of A, 3 parts of B and 4 parts of C weight 72 gm. How many gm of substance B are in the mixture?
উত্তর
9
সমাধান
Total parts = 17+3+4 = 2424 parts = 72 gm1 parts = 72/24 = 3gmnow, total substances of B = 3B = 3*3 = 9 (Ans.)
২২৮৯০
The average weight of 3 young men is 53 kg. No one of them weighs less than 51 kg. What is the maximum weight of any one man?
উত্তর
57
সমাধান
The total weight of them = 53×3 = 159 kg
Minimum weight possible for any 2 of them = 51×2 = 102 kg
Maximum weight of any 1 of them = 159 - 102 = 57 kg