To find the average of a set of numbers, we need to sum all the numbers and then divide the sum by the total count of numbers in the set.
Correct Option: A) 17
If a sum of Rs 2,000 amounts to Rs 2,360 in 3 years at a certain rate of simple interest per annum, what will the same sum amount to in 5 years if the rate of simple interest per annum remains the same?
We need to first calculate the simple interest rate per annum using the given principal, amount, and time. Once the rate is found, we can use it to calculate the amount for the same principal over a different time period (5 years).
Given:
Simple Interest \((SI) = A - P\)
\[ SI = 2360 - 2000 = \text{Rs } 360 \]The formula for simple interest is:
\[ SI = \frac{P \times R \times T}{100} \]Rearranging to find \(R\):
\[ R = \frac{SI \times 100}{P \times T} \]Substitute the values:
\[ R = \frac{360 \times 100}{2000 \times 3} = \frac{36000}{6000} = 6\% \]So, the rate of simple interest is \(6\%\) per annum.
Now, we need to find the amount for the same sum in 5 years with the same rate.
Amount \((A) = P + SI\)
\[ A = 2000 + 600 = \text{Rs } 2,600 \]Correct Option: B) Rs 2,600
The question asks to identify the specific Article of the Indian Constitution that mandates the Governor to constitute a Finance Commission for Panchayats every five years. This requires knowledge of Part IX of the Indian Constitution, which deals with Panchayats, and the specific articles related to their financial provisions.
Correct Option: B) 243 I
Which of the following terms will replace the question mark (?) in the given series to make it logically complete?
E12JZ, M16RH, U20ZP, C24HX,?
To solve this alphanumeric series, we need to identify the pattern for each component: the first letter, the number, the second letter, and the third letter. We will analyze each component separately to find the rule governing its progression.
Correct Option: D) K28PF
Refer to the given number-symbol series and answer the question that follows.
(Left) 5 ^ 3 * 4 2 $ 7 5 % 9 @ & # 8 3 = 9 3 + 2 % 8 (Right)
How many such symbols are there which are immediately preceded by a symbol and also immediately followed by a symbol?
The problem asks us to identify symbols that are immediately preceded by a symbol and immediately followed by a symbol within the given series. We need to scan the series and look for sequences of three consecutive symbols.
5 ^ 3 * 4 2 \) 7 5 % 9 @ & # 8 3 = 9 3 + 2 % 8^ 3 *: Here, ^ is a symbol, 3 is a number, * is a symbol. This does not fit the pattern "Symbol - Symbol - Symbol".3 * 4: Here, 3 is a number, * is a symbol, 4 is a number. This does not fit the pattern.* 4 2: No.4 2 \(: No.2 \) 7: No.$ 7 5: No.7 5 %: No.5 % 9: No.% 9 @: No.9 @ &: Here, 9 is a number, @ is a symbol, & is a symbol. This does not fit the pattern.@ & #: Here, @ is a symbol, & is a symbol, # is a symbol. This sequence fits the pattern "Symbol - Symbol - Symbol". The middle symbol is &. So, & is one such symbol.& # 8: Here, & is a symbol, # is a symbol, 8 is a number. This does not fit the pattern.# 8 3: No.8 3 =: No.3 = 9: No.= 9 3: No.9 3 +: No.3 + 2: No.+ 2 %: No.2 % 8: No.&.C) 1 is the correct answer because only one symbol (&) in the series is immediately preceded by a symbol (@) and immediately followed by a symbol (#).
&), not zero.The question asks for the second official language of Telangana. To answer this, one needs to know the linguistic policies and historical context of the state.
Correct Option: D) Urdu is the second official language of Telangana, declared in 2017, acknowledging its historical significance and the presence of a large Urdu-speaking population in the state.
Seven students, A, B, C, D, E, F and G, are sitting around a circular table facing the centre (but not necessarily in the same order). D is sitting second to the left of C. D is sitting to the immediate right of G. B is sitting third to the left of F. E is sitting to the immediate left of B.
Who among the following is an immediate neighbour of B and D?
The question asks about the origin country of the Buddhist teachings of Nichiren Daishonin. This requires knowledge of the history and geography of various Buddhist schools.
Correct Option: B) Japan is the correct answer because Nichiren Daishonin was a Japanese Buddhist monk who founded the Nichiren school of Buddhism in Japan during the 13th century. His teachings are deeply rooted in Japanese culture and history.
If 0.25a = 0.05b, then which of the options below gives the best approximation of the value of \( \frac{b-a}{b+a} \)?
The problem provides an equation relating two variables, \(a\) and \(b\), and asks for the approximate value of an expression involving \(a\) and \(b\). The strategy is to first find the ratio of \(a\) to \(b\) from the given equation, and then substitute this ratio into the expression to be evaluated.
The given equation is \(0.25a = 0.05b\).
To simplify, we can divide both sides by 0.05:
\[ \frac{0.25a}{0.05} = b \]\[ 5a = b \]From \(5a = b\), we can write the ratio of \(a\) to \(b\) as:
\[ \frac{a}{b} = \frac{1}{5} \]The expression to be evaluated is \( \frac{b-a}{b+a} \). To use the ratio \(\frac{a}{b}\), we can divide the numerator and the denominator of the expression by \(b\):
\[ \frac{b-a}{b+a} = \frac{\frac{b-a}{b}}{\frac{b+a}{b}} = \frac{\frac{b}{b} - \frac{a}{b}}{\frac{b}{b} + \frac{a}{b}} = \frac{1 - \frac{a}{b}}{1 + \frac{a}{b}} \]Now, substitute the value of \[\frac{a}{b} = \frac{1}{5}\] into the simplified expression:
\[ \frac{1 - \frac{1}{5}}{1 + \frac{1}{5}} = \frac{\frac{5-1}{5}}{\frac{5+1}{5}} = \frac{\frac{4}{5}}{\frac{6}{5}} \]\[ = \frac{4}{5} \times \frac{5}{6} = \frac{4}{6} = \frac{2}{3} \]The decimal value of \(\frac{2}{3}\) is approximately \(0.666...\), which can be rounded to \(0.67\).
C) 0.67 is the best approximation of the value of \( \frac{b-a}{b+a} \).
Find the missing value of weight (X) assigned if the weighted average of the data set provided below is 24.5.
| Object | A | B | C | D |
| Value of object | 15 | 2 | 30 | 43 |
| Assigned weight | 3 | 2 | x | 1 |
The problem asks us to find a missing weight (X) given a dataset of object values and their assigned weights, along with the weighted average of the entire dataset. We will use the formula for the weighted average to set up an equation and solve for X.
The missing value of weight (X) is 10.
Correct Option: D) 10