Smita can finish a work in 12 days and Sam can finish the same work in 9 days. After working together for 4 days they both leave the job. What is the fraction of unfinished work?
\( \frac{1}{2} \)
\( \frac{7}{9} \)
\( \frac{2}{9} \)
\( \frac{1}{4} \)
This problem involves calculating the work done by two individuals working together and then determining the remaining unfinished work. We will first find the individual work rates, then their combined work rate, calculate the work done in the given time, and finally find the fraction of unfinished work.
Smita can finish the work in 12 days. So, Smita's one day's work is:
\[ \text{Smita's 1 day's work} = \frac{1}{12} \]Sam can finish the work in 9 days. So, Sam's one day's work is:
\[ \text{Sam's 1 day's work} = \frac{1}{9} \]When they work together, their combined one day's work is the sum of their individual work rates:
\[ \text{Combined 1 day's work} = \frac{1}{12} + \frac{1}{9} \]To add these fractions, find a common denominator, which is 36:
\[ \text{Combined 1 day's work} = \frac{3}{36} + \frac{4}{36} = \frac{3+4}{36} = \frac{7}{36} \]They worked together for 4 days. So, the total work done in 4 days is:
\[ \text{Work done in 4 days} = 4 \times \text{Combined 1 day's work} = 4 \times \frac{7}{36} \]Simplify the expression:
\[ \text{Work done in 4 days} = \frac{28}{36} = \frac{7}{9} \]The total work is considered as 1. The fraction of unfinished work is the total work minus the work done:
\[ \text{Unfinished work} = 1 - \text{Work done} = 1 - \frac{7}{9} \]To subtract, express 1 as a fraction with denominator 9:
\[ \text{Unfinished work} = \frac{9}{9} - \frac{7}{9} = \frac{9-7}{9} = \frac{2}{9} \]Thus, the fraction of unfinished work is \( \frac{2}{9} \).
C) \( \frac{2}{9} \)
This is a blood relation problem. We need to decode the statement made by A to C about B to establish the relationship between C and B. We will break down the statement "His mother is the only daughter of your father" part by part.
Correct Option: A) Mother. Based on the analysis, C is the mother of B.
If x is a prime number, LCM of x and its successive number would be
To find the Least Common Multiple (LCM) of two numbers, we need to understand their relationship. If two numbers are coprime (i.e., their greatest common divisor is 1), their LCM is simply the product of the two numbers. We will apply this principle to a prime number and its successive number.
Correct Option: C) The LCM of \(x\) and its successive number \(x+1\) is \(x(x+1)\) because \(x\) and \(x+1\) are consecutive integers and thus coprime. The LCM of two coprime numbers is their product.
Both conclusions I and II follow
This problem involves analyzing logical statements and conclusions using Venn diagrams or by direct logical deduction. We need to determine which conclusions necessarily follow from the given statements.
Let's represent the statements using Venn diagrams or logical relationships:
C) Both conclusions I and II follow
As analyzed above, both conclusion I and conclusion II can be logically deduced from the given statements.
Find the value of: \(\frac{(0.0112 - 0.0012)\times 0.14 + 0.25\times 0.2}{0.02\times 0.01}\)
To solve this problem, we need to simplify the given expression by performing the arithmetic operations (subtraction, multiplication, and division) in the correct order. We will first simplify the numerator and the denominator separately and then perform the final division.
The first part of the numerator is \((0.0112 - 0.0012)\).
\[ 0.0112 - 0.0012 = 0.0100 \]The numerator becomes \(0.0100 \times 0.14 + 0.25 \times 0.2\).
First multiplication:
\[ 0.0100 \times 0.14 = 0.0014 \]Second multiplication:
\[ 0.25 \times 0.2 = 0.050 \]Now, add the results from step 2:
\[ 0.0014 + 0.050 = 0.0514 \]So, the numerator is \(0.0514\).
The denominator is \(0.02 \times 0.01\).
\[ 0.02 \times 0.01 = 0.0002 \]Now, divide the simplified numerator by the simplified denominator:
\[ \frac{0.0514}{0.0002} \]To make the division easier, we can multiply both the numerator and the denominator by \(10000\) to remove the decimal points:
\[ \frac{0.0514 \times 10000}{0.0002 \times 10000} = \frac{514}{2} \]Now, perform the division:
\[ \frac{514}{2} = 257 \]Correct Option: A) 257
The question asks to identify gases responsible for the greenhouse effect. This requires knowledge of common greenhouse gases and their roles in trapping heat in the Earth's atmosphere.
Both carbon dioxide and methane are major contributors to the greenhouse effect.
The problem presents a pattern where symbols are assigned numerical values. We need to decode the value of each symbol from the given equations and then use these values to find the number represented by the new sequence of symbols.
From the first given equation, \(\Delta o = 52\), we can deduce the individual values of the symbols. Assuming each symbol corresponds to a single digit, we have:
From the second given equation, \(\square \# = 43\), we can deduce the individual values of the symbols:
Now we need to find the value of \(\# \Delta \square\). We substitute the values we found for each symbol:
Combining these digits in the order given, \(\# \Delta \square\) becomes \(354\).
D) 354 — By assigning each symbol a unique digit based on the given patterns, we find that \(\Delta = 5\), \(o = 2\), \(\square = 4\), and \(\# = 3\). Therefore, \(\# \Delta \square\) corresponds to the number \(354\).
If \( \frac{1}{4} \)th of the wall is painted blue, \( \frac{1}{2} \) is painted yellow and remaining 3 m is painted white, what is the length of the wall?
To find the total length of the wall, we need to determine what fraction of the wall the remaining 3 meters represents. We can do this by subtracting the painted fractions (blue and yellow) from the total length of the wall (which is 1 or \( \frac{1}{1} \)). Once we know the fraction corresponding to 3 meters, we can calculate the total length.
Let the total length of the wall be \(L\) meters.
The fraction of the wall painted blue is \( \frac{1}{4} \).
The fraction of the wall painted yellow is \( \frac{1}{2} \).
First, find the total fraction of the wall painted blue and yellow:
\[ \text{Fraction painted (blue + yellow)} = \frac{1}{4} + \frac{1}{2} \]To add these fractions, find a common denominator, which is 4:
\[ \frac{1}{4} + \frac{2}{4} = \frac{1+2}{4} = \frac{3}{4} \]So, \( \frac{3}{4} \) of the wall is painted blue and yellow.
The remaining part of the wall is painted white. To find the fraction of the wall painted white, subtract the painted fraction from the total length (which is 1):
\[ \text{Fraction painted white} = 1 - \frac{3}{4} \]Convert 1 to a fraction with denominator 4:
\[ \frac{4}{4} - \frac{3}{4} = \frac{4-3}{4} = \frac{1}{4} \]So, \( \frac{1}{4} \) of the wall is painted white.
We are given that the remaining 3 meters of the wall is painted white. Therefore, \( \frac{1}{4} \) of the total length of the wall is equal to 3 meters:
\[ \frac{1}{4} \times L = 3 \]To find the total length \(L\), multiply both sides by 4:
\[ L = 3 \times 4 \]\[ L = 12 \text{ meters} \]The total length of the wall is 12 meters.
Correct Option: D) 12
This is a coding-decoding question based on directions. We need to identify the standard direction in which the sun rises and then apply the given coding rules to find its coded equivalent.
Correct Option: C) North
The question asks to identify the last Mughal Emperor. This requires knowledge of the history of the Mughal Empire and its rulers.
Correct Option: D) Bahadur Shah was the last Mughal Emperor. He reigned from 1837 to 1857 and was exiled by the British after the 1857 Sepoy Mutiny (First War of Indian Independence).