This problem involves setting up and solving a system of two linear equations based on the given age relationships at different points in time. We will define variables for the father's and son's present ages and then translate the given conditions into algebraic equations.
Let the present age of the father be \(F\) years.
Let the present age of the son be \(S\) years.
Five years from now:
According to the problem, father’s age will be three times the age of his son:
\[ F + 5 = 3(S + 5) \]\[ F + 5 = 3S + 15 \]\[ F - 3S = 15 - 5 \]\[ F - 3S = 10 \quad \text{(Equation 1)} \]Five years ago:
According to the problem, father was seven times as old as his son:
\[ F - 5 = 7(S - 5) \]\[ F - 5 = 7S - 35 \]\[ F - 7S = -35 + 5 \]\[ F - 7S = -30 \quad \text{(Equation 2)} \]We have two linear equations:
Equation 1: \(F - 3S = 10\)
Equation 2: \(F - 7S = -30\)
Subtract Equation 2 from Equation 1:
\[ (F - 3S) - (F - 7S) = 10 - (-30) \]\[ F - 3S - F + 7S = 10 + 30 \]\[ 4S = 40 \]\[ S = \frac{40}{4} \]\[ S = 10 \]Using Equation 1:
\[ F - 3(10) = 10 \]\[ F - 30 = 10 \]\[ F = 10 + 30 \]\[ F = 40 \]The present age of the father is 40 years, and the present age of the son is 10 years.
Correct Option: D) 40 and 10
The question asks to identify the incorrect statement about photosynthesis. We need to analyze each option based on the biochemical process of photosynthesis.
A) Photosynthesis involves oxidation of carbon dioxide to carbohydrates — This statement is incorrect. In photosynthesis, carbon dioxide (\(\text{CO}_2\)) is reduced to form carbohydrates (\(\text{C}_6\text{H}_{12}\text{O}_6\)). Reduction involves the gain of electrons or hydrogen atoms, while oxidation is the loss of electrons or gain of oxygen. The water molecules are oxidized, releasing electrons and oxygen, while carbon dioxide is reduced.
The problem asks us to find the ratio \(x:y\) given a relationship between percentages of \(x\) and \(y\). We will convert the percentages into fractions and then algebraically manipulate the equation to express \(x/y\) as a simplified fraction.
First, write the given relationship as an equation:
\[ 35\% \text{ of } x = 40\% \text{ of } y \]Convert the percentages to decimal or fractional form. Recall that \(P\% = P/100\):
\[ \frac{35}{100} \times x = \frac{40}{100} \times y \]Simplify the fractions:
\[ \frac{7}{20} \times x = \frac{2}{5} \times y \]To find the ratio \(x:y\), we need to express it as \(x/y\). Divide both sides by \(y\) and by \(\frac{7}{20}\) (or multiply by \(\frac{20}{7}\)):
\[ \frac{x}{y} = \frac{\frac{2}{5}}{\frac{7}{20}} \]Simplify the complex fraction by multiplying the numerator by the reciprocal of the denominator:
\[ \frac{x}{y} = \frac{2}{5} \times \frac{20}{7} \]Perform the multiplication and simplify:
\[ \frac{x}{y} = \frac{2 \times 20}{5 \times 7} = \frac{40}{35} \]Reduce the fraction to its simplest form by dividing both the numerator and the denominator by their greatest common divisor, which is 5:
\[ \frac{x}{y} = \frac{40 \div 5}{35 \div 5} = \frac{8}{7} \]Therefore, the ratio \(x:y\) is \(8:7\).
A) \(8:7\) is the correct ratio as derived from the given equation.
The question asks to identify the sport played by Padma Shri 2022 awardee Vandana Kataria. This requires general knowledge about prominent Indian sports personalities and their respective fields.
Correct Option: A) Vandana Kataria is an Indian field hockey player. She was part of the Indian women's national field hockey team and was awarded the Padma Shri in 2022 for her contributions to the sport. She is known for her role as a forward.
The problem asks us to identify the largest and smallest numbers from a given set of three-digit numbers, then extract specific digits from them, and finally perform an addition operation. We need to follow the steps carefully to avoid errors in identifying the numbers and their digits.
D) 8 is the correct resultant when the second digit of the largest number (5) is added to the first digit of the smallest number (3).
The question asks about the essential component for glucose breakdown in human cells to produce energy. This process is known as cellular respiration. We need to identify which of the given options plays a crucial role in this energy-generating pathway.
Correct Option: A) Oxygen is essential for the complete and efficient breakdown of glucose in human cells through aerobic respiration, leading to the production of a large amount of energy (ATP).
The problem describes a linear arrangement of persons facing North. We need to determine the total number of persons based on the given relative positions. We will build the arrangement step-by-step using the clues provided.
D _ _ _ _ GH G EE G HD _ _ _ _ H G ED _ _ _ _ E G HH G E, then C must be to the immediate right of E. So, H G E C. The full arrangement becomes: D _ _ _ _ H G E CE G H, then C must be to the immediate right of E. This means C is between E and G: E C G H. However, the clue states that G is an immediate neighbour of E. If C is between E and G, then G is not an immediate neighbour of E. Therefore, possibility (b) is incorrect.D _ _ _ _ H G E C.H G E C.D) Nine. Based on the step-by-step construction, the final arrangement has 9 persons.
This question asks to identify the gas evolved when zinc reacts with hydrochloric acid. This is a classic example of a single displacement reaction where a more reactive metal displaces hydrogen from an acid.
Correct Option: D) \(\text{H}_2\) is hydrogen gas, which is evolved when zinc reacts with hydrochloric acid.
The question asks for the specific term used when companies sell multiple products together at a single price. We need to identify the pricing strategy that matches this description from the given options.
Correct Option: C) Bundle pricing is a pricing method in which companies group several products together and sell them at a single price. This strategy is often used to increase sales volume, clear inventory, or offer greater value to customers.
The problem presents a series of number pairs and asks us to find the missing number in the last pair based on the relationship observed in the previous pairs. We need to identify a consistent mathematical operation or pattern that connects the first number to the second number in each given pair.
The missing number is 5.
D) 5 — The pattern established is that the first number is equal to the fourth power of the second number minus one. That is, \( \text{First Number} = (\text{Second Number})^4 - 1 \). Applying this to 624, we get \( 624 = x^4 - 1 \), which leads to \( x^4 = 625 \), and thus \( x = 5 \).