In a certain office (1/3) of the worker are women (1/2) of the women are married and (1/3) of the married women have children. If (3/4) of the man are married and (2/3) of the married men have children. What part of workers are without children?

According to the question.
([P + (P x 6 x T)/100] - [P + (P x 1 x T)/100] = 600 - 200
? 5PT/100 = 400
? PT = 8000

Again, for 6% rate,
SI = PTR/100 = (8000 x 6)/100 = ? 480
? Sum = 600 - 480 = ? 120
As we have, PT = 8000
? T = 8000/120 = 200/3 = 66²/₃ yr

Let us assume that Arun uses N units of petrol everyday. so the amount of of petrol in the tank when it is full will be 10N. If he starts using 25% more petrol everyday. then the units of petrol he now use everyday will be
N(1 + 25/100) = 1.25N

So, the number of days his petrol will now last will be equal to (amount of petrol in tank) / (number of units used everyday)
= (10N) / (1.25N) = 10 / 1.25
= 8 days

7^8.9 ÷ (343)^1.7 x (49)^4.8 = 7^?
Apply the law of Fractional Exponents and Laws of Exponents
(a^m)(aⁿ) = a^m+n
a^m÷aⁿ=a^m?n
a^m/aⁿ=a^m?n
(a^m)ⁿ = a^mn
7^8.9 ÷ (343)^1.7 x (49)^4.8 = 7^?
? 7^8.9 ÷ (7³)^1.7 x (7²)^4.8 = 7^?
? 7^8.9 ÷ 7^5.1 x 7^9.6 = 7^?
? 7^{8.9 - 5.1 + 9.6} = 7^?
? 7^{18.5 - 5.1} = 7^?
? ? = 13.4

Given that :- sum of the roots = 6
And Product of two roots = -16
The required quadratic equation is x² ? (sum of the roots) x + (product of the roots) = 0
? x² - 6x - 16 = 0

As per the given above question , we have
Let, x = 6 + ?6 + ?6 + ?6 +........
On squaring both sides, we have
x² = 6 + ?6 + ?6 + ?6 +........
? x² = 6 + x
? x² - x - 6 = 0
? x² - 3x + 2x - 6 = 0
? x( x - 3 ) + 2( x - 3 ) = 0
? ( x - 3 ) ( x + 2 ) = 0
? x = 3 and x ? ?2 because numbers are positive.
Thus , correct answer will be 3 .

Given in the question ,
n(X ?Y) = 18, n(X) = 8, n(Y) = 15.
Using the formula
n(X ? Y) = n(X) + n(Y) ? n(X ? Y), we get n(X ? Y) = 8 + 15 ? 18 = 5.

Draw a figure and calculate.
Number of people speak English only
= 50 ? (10 + 25)
= 15

A ? U = {2, 4, 7} ? {2, 3, 4, 5, 6, 7, 8, 9, 10, 11}
A ? U = {2, 4, 7};
B ? C = {3, 5, 7, 9, 11} ? {7, 8, 9, 10, 11}.
B ? C = {3, 5, 7, 8, 9, 10, 11}.
Then (A ? U) ? (B ? C) = {2, 4, 7,} ? {3, 5, 7, 8, 9, 10, 11}
(A ? U) ? (B ? C) = {7}.

17^3.5 x 17^7.3 ÷ 17^4.2 = 17^?
Apply the Laws of Exponents ::
(a^m) x (aⁿ) = a^m+n
Fractional Exponents ::
a^m÷ a ⁿ=a^m?n
? 17^{3.5 + 7.3 - 4.2} = 17^?
? 17^6.6 = 17^?
? ? = 6.6