This problem involves compound interest. We need to find the initial amount given to Shan, given that the total amount is divided between two sons, Shan and Piyush, and their final amounts after different time periods are equal. We will use the compound interest formula to set up an equation and solve for the unknown principal amount given to Shan.
Let the amount Rishi gave to Shan be \(P_S\) and the amount given to Piyush be \(P_P\).
The total amount is ₹1,612, so:
\[ P_S + P_P = 1612 \quad \text{(Equation 1)} \]The rate of interest is 8% per annum, compounded annually. The formula for the amount \(A\) after \(t\) years with principal \(P\) and rate \(r\) is:
\[ A = P \left(1 + \frac{r}{100}\right)^t \]For Shan, the time period is 19 years. So, the amount Shan gets after 19 years is:
\[ A_S = P_S \left(1 + \frac{8}{100}\right)^{19} = P_S (1.08)^{19} \quad \text{(Equation 2)} \]For Piyush, the time period is 20 years. So, the amount Piyush gets after 20 years is:
\[ A_P = P_P \left(1 + \frac{8}{100}\right)^{20} = P_P (1.08)^{20} \quad \text{(Equation 3)} \]According to the problem, Shan and Piyush got the same amount after their respective time periods. So, \(A_S = A_P\):
\[ P_S (1.08)^{19} = P_P (1.08)^{20} \]Now, we can simplify this equation to find a relationship between \(P_S\) and \(P_P\):
\[ P_S = P_P \frac{(1.08)^{20}}{(1.08)^{19}} \]\[ P_S = P_P (1.08) \]\[ P_S = 1.08 P_P \quad \text{(Equation 4)} \]Substitute Equation 4 into Equation 1:
\[ 1.08 P_P + P_P = 1612 \]\[ (1.08 + 1) P_P = 1612 \]\[ 2.08 P_P = 1612 \]Solve for \(P_P\):
\[ P_P = \frac{1612}{2.08} \]\[ P_P = \frac{161200}{208} \]\[ P_P = 775 \]Now, substitute the value of \(P_P\) back into Equation 4 to find \(P_S\):
\[ P_S = 1.08 \times 775 \]\[ P_S = 837 \]So, Rishi gave ₹837 to Shan.
D) ₹837
This is a coding-decoding question based on common words. We need to find the code for the word 'are' by comparing the given coded statements.
Correct Option: A) zl
The question asks to identify the MS Word feature that controls the spacing between the text and the edges of the page. This is a fundamental document formatting concept.
Correct Option: B) Margins — In MS Word, "Margins" is the specific feature that allows users to define the amount of space between the text and the top, bottom, left, and right edges of the page. Adjusting margins directly impacts how much text fits on a page and the overall layout.
The question asks about the specific wavelength and type of laser used in a standard CD-ROM drive. This is a factual recall question related to the technology of optical storage devices. We need to identify the correct laser specifications for CD-ROMs.
B) 780 nm; infrared laser — This option correctly identifies both the wavelength (780 nm) and the type (infrared) of the laser used in standard CD-ROM drives. This wavelength was chosen for its ability to read the data density of CDs effectively.
The fraction equivalent to 8.27272... is:
\( \frac{91}{11} \)
\( \frac{89}{8} \)
\( \frac{84}{17} \)
\( \frac{83}{12} \)
To convert a repeating decimal into a fraction, we can use an algebraic method. We set the given decimal equal to a variable, multiply by powers of 10 to align the repeating part, and then subtract the equations to eliminate the repeating decimal.
Correct Option: A) \( \frac{91}{11} \)
We are given the ratios of incomes and expenditures, along with the savings of Seema and Darshan. We can set up algebraic equations based on the fundamental relationship: Income = Expenditure + Savings. By solving these equations, we can find the individual expenditures and then their total expenditure.
Define variables based on given ratios:
Let the income of Seema be \(7x\) and Darshan be \(8x\).
Let the expenditure of Seema be \(11y\) and Darshan be \(16y\).
Formulate equations using the Income-Expenditure-Savings relationship:
For Seema:
\[ \text{Income}_{\text{Seema}} = \text{Expenditure}_{\text{Seema}} + \text{Savings}_{\text{Seema}} \] \[ 7x = 11y + 15000 \quad \text{(Equation 1)} \]For Darshan:
\[ \text{Income}_{\text{Darshan}} = \text{Expenditure}_{\text{Darshan}} + \text{Savings}_{\text{Darshan}} \] \[ 8x = 16y + 9000 \quad \text{(Equation 2)} \]Solve the system of linear equations:
We can eliminate \(x\) from the two equations. Multiply Equation 1 by 8 and Equation 2 by 7:
Equation 1 \(\times 8\):
\[ 56x = 88y + 120000 \quad \text{(Equation 3)} \]Equation 2 \(\times 7\):
\[ 56x = 112y + 63000 \quad \text{(Equation 4)} \]Subtract Equation 4 from Equation 3 (or vice versa):
\[ (88y + 120000) - (112y + 63000) = 0 \] \[ 88y + 120000 - 112y - 63000 = 0 \] \[ -24y + 57000 = 0 \] \[ 24y = 57000 \] \[ y = \frac{57000}{24} \] \[ y = 2375 \]Calculate the expenditures:
Expenditure of Seema \(= 11y = 11 \times 2375 = 26125\)
Expenditure of Darshan \(= 16y = 16 \times 2375 = 38000\)
Calculate the total expenditure:
Total expenditure \(= \text{Expenditure}_{\text{Seema}} + \text{Expenditure}_{\text{Darshan}}\)
\[ \text{Total expenditure} = 26125 + 38000 = 64125 \]Correct Option: C) 64,125
The problem involves ratios and differences. We are given the ratio of marbles in four boxes and the difference in the number of marbles between two specific boxes. We need to find the total number of marbles. We can represent the number of marbles in each box using a common multiplier based on the given ratio and then use the difference to find the value of this multiplier.
Represent the number of marbles using a common multiplier:
Let the common multiplier for the ratio be \(x\). The marbles in boxes A, B, C, and D can be represented as:
Use the given difference to find the value of \(x\):
We are told that box B has 400 less marbles than box D. This can be written as an equation:
Solve for \(x\):
\[ 2x = 400 \]\[ x = \frac{400}{2} \]\[ x = 200 \]Calculate the total number of marbles:
The total number of marbles in all boxes is the sum of marbles in A, B, C, and D:
Substitute the value of \(x\) into the total marbles equation:
\[ \text{Total Marbles} = 21 \times 200 \]\[ \text{Total Marbles} = 4200 \]C) 4200 is the total number of marbles in all the boxes.
A) 4000 — This would be the total if \(x\) was approximately 190.47, or if the total ratio sum was 20 instead of 21. This is incorrect as per our calculation.
B) 4100 — This would be the total if \(x\) was approximately 195.23. This is incorrect.
D) 3900 — This would be the total if \(x\) was approximately 185.71. This is incorrect.
This is a logical reasoning problem involving the arrangement of people on different floors of a building. We need to deduce the exact floor on which each person lives based on the given clues and then identify who lives on floor number 3.
There are six floors, numbered 1 to 6 from bottom to top.
Clue 1: Only M lives above N.
This implies that M is on the topmost floor (floor 6) and N is on floor 5. If anyone else lived above N, the condition "Only M lives above N" would be violated.
Clue 2: Z lives immediately below N.
Since N is on floor 5, Z must be on floor 4.
Clue 3: Only P lives below O.
This means O is on floor 2 and P is on floor 1. If anyone else lived below O, the condition "Only P lives below O" would be violated.
Now, let's consolidate the information we have:
The remaining person is Y, and the only remaining floor is floor 3. Therefore, Y must live on floor 3.
The question asks who lives on floor numbered 3. Based on our deductions, Y lives on floor 3.
B) Y — As determined in the step-by-step analysis, Y is the only person left to occupy floor 3 after placing M, N, Z, O, and P according to the given conditions.
The problem asks us to identify the letter-cluster pair that does not follow the same pattern as the others, based on the English alphabetical order. We need to find the relationship between the letters in each pair (e.g., MO - KM) and then determine which option deviates from that pattern.
Options A, C, and D follow a consistent pattern:
Option B follows a different pattern:
Therefore, Option B does not belong to the group.
B) CG - LP