This is a blood relation problem where symbols represent relationships. We need to decode the given expression 'M + N ÷ O – P × Q' step-by-step to determine the relationship between M and Q.
From the combined relationships:
Therefore, M is the mother of P's father (N), and P is Q's wife. So, M is the mother of Q's wife's father. This means M is Q's wife's father's mother.
D) Wife's father's mother. As derived, M is the mother of N, N is the father of P, and P is the wife of Q. Thus, M is the mother of P's father, and P is Q's wife. So, M is Q's wife's father's mother.
This problem involves determining the relative positions of towns based on a series of directional statements. The best way to solve this is to draw a diagram or visualize the positions on a coordinate plane, starting with one town and placing others relative to it. We need to find the position of Town G with respect to Town I.
Let's consolidate these positions:
Now, let's place them relative to each other to determine the final relationship:
From statement 2 and 3, we can infer that H is to the west of G, and F is to the south of G. So, H, G, and F form a rough L-shape, with G at the corner. H is left of G, F is below G.
From statement 1, E is to the east of F. So, E is to the right of F.
From statement 4, I is to the east of H. This means I is to the right of H.
Now, consider the last statement: Town E is to the south-west of Town I. This implies that I is relatively far north-east compared to E. Since E is east of F and F is south of G, E is south-east of G. If I is north-east of E, and I is also east of H, then G must be positioned such that it is west of I.
Let's visualize:
H --- G | | | F --- E
Now, place I. We know I is east of H. We also know E is south-west of I. This means I is north-east of E. Given E is east of F and F is south of G, E is roughly south-east of G. For I to be north-east of E, and also east of H, the arrangement becomes:
H --- G --- I (I is east of H, and could be east of G or north-east of G)
|
F --- E
The condition "Town E is to the south-west of Town I" confirms that I is positioned such that it is to the north-east of E. Since G is north of F and F is west of E, G is north-west of E. If I is north-east of E, and G is north-west of E, then G must be to the west of I.
Let's draw a possible arrangement:
I
/
G ---
|
F -- E
In this arrangement:
From this visualization, Town G is clearly to the west of Town I.
Correct Option: D) West
To find Ashish's total savings in a year, we first need to calculate his monthly savings. We subtract his monthly expenses (house rent and bills) from his monthly salary. Then, we multiply this monthly savings by the number of months in a year, keeping in mind that he spends all his savings in one month (his birthday month).
Monthly expenses = House rent + Bills
\[ \text{Monthly expenses} = \text{₹}4,000 + \text{₹}1,500 = \text{₹}5,500 \]Monthly savings = Monthly salary - Monthly expenses
\[ \text{Monthly savings} = \text{₹}11,000 - \text{₹}5,500 = \text{₹}5,500 \]Since Ashish spends all his savings in his birthday month, he only saves for 11 months out of the year.
\[ \text{Savings for 11 months} = \text{Monthly savings} \times 11 \]\[ \text{Savings for 11 months} = \text{₹}5,500 \times 11 = \text{₹}60,500 \]His total savings in a year will be the savings accumulated over these 11 months, as the savings from the birthday month are spent.
\[ \text{Total savings in a year} = \text{₹}60,500 \]C) ₹60,500 is the correct answer. This is calculated by finding the monthly savings and then multiplying it by 11 months, as one month's savings are spent on birthday celebrations.
Find the value of m for which it satisfies \(\left(\frac{21}{8}\right)^{12}\times\left(\frac{8}{21}\right)^{14}\times\left(\frac{21}{8}\right)^{14}=\left(\frac{8}{21}\right)^{9m+20}\).
-\( \frac{25}{9} \)
-\( \frac{32}{9} \)
-\( \frac{22}{9} \)
-\( \frac{37}{9} \)
The problem involves solving an exponential equation. The key is to express all terms with the same base. We will use the properties of exponents, specifically \(a^{-n} = \frac{1}{a^n}\) and \((a^m)(a^n) = a^{m+n}\), to simplify the equation and then equate the exponents.
The given equation is:
\[ \left(\frac{21}{8}\right)^{12}\times\left(\frac{8}{21}\right)^{14}\times\left(\frac{21}{8}\right)^{14}=\left(\frac{8}{21}\right)^{9m+20} \]Our goal is to make the bases on both sides of the equation the same. Let's choose \(\frac{8}{21}\) as the common base. We know that \[\frac{21}{8} = \left(\frac{8}{21}\right)^{-1}\].
Substitute this into the equation:
\[ \left(\left(\frac{8}{21}\right)^{-1}\right)^{12}\times\left(\frac{8}{21}\right)^{14}\times\left(\left(\frac{8}{21}\right)^{-1}\right)^{14}=\left(\frac{8}{21}\right)^{9m+20} \]Apply the power of a power rule \(((a^m)^n = a^{mn})\):
\[ \left(\frac{8}{21}\right)^{-12}\times\left(\frac{8}{21}\right)^{14}\times\left(\frac{8}{21}\right)^{-14}=\left(\frac{8}{21}\right)^{9m+20} \]Now, apply the product rule for exponents \((a^m \times a^n = a^{m+n})\) on the left side:
\[ \left(\frac{8}{21}\right)^{-12+14-14}=\left(\frac{8}{21}\right)^{9m+20} \]Simplify the exponent on the left side:
\[ \left(\frac{8}{21}\right)^{-12}=\left(\frac{8}{21}\right)^{9m+20} \]Since the bases are now equal, we can equate the exponents:
\[ -12 = 9m+20 \]Solve for \(m\):
\[ 9m = -12 - 20 \]\[ 9m = -32 \]\[ m = -\frac{32}{9} \]B) \(-\frac{32}{9}\) is the correct value for \(m\) that satisfies the given equation.
This problem involves basic percentage calculations. We are given the percentage of income saved and the absolute value of expenditure. We need to find the total income. The key is to understand that income is divided into savings and expenditure, and if savings are 40%, then expenditure must be the remaining percentage.
If a person saves 40% of his income, then the remaining percentage is spent as expenditure.
\[ \text{Percentage of Expenditure} = 100\% - \text{Percentage of Savings} \]\[ \text{Percentage of Expenditure} = 100\% - 40\% = 60\% \]We are given that the expenditure is ₹480. This amount corresponds to 60% of the total income.
\[ 60\% \text{ of Income} = \text{₹}480 \]Let the total income be \(I\). We can set up the equation:
\[ 0.60 \times I = 480 \]To find the total income, divide the expenditure by its percentage (in decimal form).
\[ I = \frac{480}{0.60} \]\[ I = \frac{480}{\frac{60}{100}} \]\[ I = \frac{480 \times 100}{60} \]\[ I = \frac{48000}{60} \]\[ I = 800 \]Thus, the person's income is ₹800.
Correct Option: A) 800
To determine which number is divisible by 38, we can use the divisibility rule. A number is divisible by 38 if it is divisible by both its prime factors, 2 and 19. Alternatively, we can directly perform division for each option.
Correct Option: A) 1938 is divisible by 38 because \(1938 \div 38 = 51\).
This problem involves work and time. We need to find the time taken by B alone to complete the work. We can solve this by calculating the individual work rates (amount of work done per hour) and then combining them.
Calculate the work rate of A:
A can do a piece of work in 57 hours.
So, A's 1-hour work rate is:
Calculate the combined work rate of A and C:
A and C together can do the work in 19 hours.
So, (A + C)'s 1-hour work rate is:
Calculate the work rate of C alone:
We can find C's work rate by subtracting A's work rate from (A + C)'s work rate:
Calculate the combined work rate of B and C:
B and C together can do the work in 28 hours.
So, (B + C)'s 1-hour work rate is:
Calculate the work rate of B alone:
We can find B's work rate by subtracting C's work rate from (B + C)'s work rate:
To subtract these fractions, find a common denominator, which is \(28 \times 57 = 1596\):
\[ \text{B's work rate} = \frac{57}{28 \times 57} - \frac{2 \times 28}{57 \times 28} \]\[ \text{B's work rate} = \frac{57}{1596} - \frac{56}{1596} \]\[ \text{B's work rate} = \frac{1}{1596} \text{ part of work per hour} \]Calculate the time B alone takes to do the work:
If B does \(1/1596\) of the work in 1 hour, then B will take 1596 hours to complete the entire work.
C) 1596
The question asks to identify the plateau through which the Damodar River flows. This requires knowledge of the geographical location and course of the Damodar River and the major plateaus in India.
Correct Option: D) The Damodar River originates in and flows through the Chhotanagpur Plateau. This plateau is known for its rich mineral resources and is often referred to as the "Ruhr of India." The Damodar Valley Corporation (DVC), one of India's earliest multi-purpose river valley projects, was established on this river.
To solve this problem, we need to identify the highest and lowest numbers from the given set of three-digit numbers. Then, we extract the first digit of the highest number and the third digit of the lowest number. Finally, we add these two digits to find the resultant value.
B) 18 is the correct answer because the first digit of the highest number (993) is 9, and the third digit of the lowest number (169) is 9. Adding these two digits gives \(9 + 9 = 18\).
To solve this problem, we need to scan the given series from left to right and identify all symbols. For each identified symbol, we then check if the element immediately preceding it is an even number and if the element immediately following it is an odd number. We count how many times this specific condition is met.
C) One. There is only one symbol '$' which is immediately preceded by an even number (8) and immediately followed by an odd number (7).