We are given the current ages of Hema and Roja. We need to find out how many years ago their ages were in a specific ratio. We can set up an equation by subtracting an unknown number of years from their current ages and equating the ratio to the given ratio.
Let Hema's current age be \(H = 48\) years.
Let Roja's current age be \(R = 32\) years.
Let \(x\) be the number of years ago when the ratio of their ages was 5 : 3.
At that time, Hema's age would have been \((48 - x)\) years.
At that time, Roja's age would have been \((32 - x)\) years.
According to the problem, the ratio of their ages at that time was 5 : 3. So, we can write the equation:
\[ \frac{48 - x}{32 - x} = \frac{5}{3} \]Now, we solve this equation for \(x\):
\[ 3(48 - x) = 5(32 - x) \]\[ 144 - 3x = 160 - 5x \]Rearrange the terms to solve for \(x\):
\[ 5x - 3x = 160 - 144 \]\[ 2x = 16 \]\[ x = \frac{16}{2} \]\[ x = 8 \]So, 8 years ago, the ratio of their ages was 5 : 3.
Let's verify the ages 8 years ago:
The ratio of their ages: \[\frac{40}{24} = \frac{5 \times 8}{3 \times 8} = \frac{5}{3}\]. This matches the given ratio.
Correct Option: C) 8 years
The problem asks for the cost of painting the outer surface of a cuboidal iron storage space that is open at the top. We need to calculate the total surface area to be painted and then multiply it by the given rate per square meter.
The total cost of painting the outer surface is ₹2046.
B) 2,046 — This matches our calculated cost of ₹2046.
To solve this direction sense problem, we need to track Puneet's movements and the direction he is facing after each turn. We can visualize this by drawing a path or simply by noting the current direction at each step.
After all the movements and turns, Puneet is facing West.
Correct Option: A) West
The problem asks us to identify how many even numbers in the given series are immediately preceded and followed by an odd number. This means we are looking for a pattern of "Odd Number - Even Number - Odd Number" in the series.
D) Five. There are five such even numbers in the series that are immediately preceded and followed by an odd number: 2 (in 923), 2 (in 321), 6 (in 567), 4 (in 943), and 6 (in 363).
The question asks to identify the medical imaging technique that uses a weak magnetic field produced inside the body to obtain images of different body parts. We need to evaluate each option based on its underlying principle.
Correct Option: D) MRI scan
The question asks for the correct statement about the Mayor in the context of Indian Municipal Corporations. We need to evaluate each option based on the constitutional provisions and common practices regarding urban local self-government in India.
Correct Option: D) Mayor is the head of the Municipal Corporation. The Mayor is the first citizen of the city and the political head of the Municipal Corporation. They preside over the meetings of the corporation and represent the city.
The question asks to identify the scientific body in India that annually awards the Shanti Swarup Bhatnagar Prize for Science and Technology. This requires knowledge of major scientific organizations in India and their associated awards.
Correct Option: C) Council of Scientific and Industrial Research (CSIR)
The Shanti Swarup Bhatnagar Prize for Science and Technology is indeed awarded annually by the Council of Scientific and Industrial Research (CSIR) for notable and outstanding research, applied or fundamental, in various branches of science and technology.
To determine if a number is divisible by 9, we use the divisibility rule for 9. This rule states that a number is divisible by 9 if the sum of its digits is divisible by 9.
Correct Option: A) 3132
The problem presents an analogy where the relationship between the first and second terms, and the fifth and sixth terms, must be identified and applied to find the missing third term related to the fourth term. We need to find a mathematical pattern or operation that transforms the first number into the second, and the fifth into the sixth, and then apply that same pattern to the third number to find the missing fourth number.
The first number is 7, and the second number is 4096.
We need to find a relationship between 7 and 4096. Let's consider powers of numbers related to 7.
If we take \(7-1 = 6\), then \(6^5 = 7776\), which is not 4096.
If we take \(7-1 = 6\), and consider powers of 4, we know that \(4^6 = 4096\).
This suggests a pattern where the first number is used to derive the exponent, and the base might be a fixed number, or derived from the first number.
Let's try a different approach: The second term is a power of some base. We know \(2^{12} = 4096\), \(4^6 = 4096\), \(8^4 = 4096\), \(16^3 = 4096\), \(64^2 = 4096\).
Consider the relationship: \((N-3)^{(N-1)}\). For \(N=7\), this would be \((7-3)^{(7-1)} = 4^6 = 4096\). This matches the first pair.
The first number is 4, and the second number is 1.
Using the pattern \((N-3)^{(N-1)}\) for \(N=4\):
\[ (4-3)^{(4-1)} = 1^3 = 1 \]This matches the third pair. So, the established pattern is \((N-3)^{(N-1)}\).
The first number is 6. We need to find the missing second term using the pattern \((N-3)^{(N-1)}\).
For \(N=6\):
\[ (6-3)^{(6-1)} = 3^5 \]Now, calculate \(3^5\):
\[ 3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 9 \times 9 \times 3 = 81 \times 3 = 243 \]Therefore, the missing term is 243.
C) 243 is the correct answer, as it follows the established pattern \((N-3)^{(N-1)}\).
Select the option that represents the letters that, when placed from left to right in the same sequence in the blanks below, will complete the letter series.
FG_C_IQ_SF_SCAIQ_SF_SC_I_PS
The problem asks us to identify the sequence of letters that completes a given letter series. This typically involves finding a repeating pattern or a logical progression within the series. We will analyze the given series and the options to find the repeating block.
A) SAPGPGAQ is the correct option. When these letters are placed in the blanks, the series becomes FGSCAIQPSFGSCAIQPSFGSCAIQPS, which is a clear repetition of the 9-letter block "FGSCAIQPS\