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In the following questions, two statements numbered I and II are given. On solving them, we get quantities I and II respectively. Solve for both the quantities and choose the correct option.
Quantity I: Difference between CI and SI for 3 years at the rate of 12% per annum for principal 150000.
Quantity II: Number of students in Navodaya Vidyalaya Delhi during 2013 was 5600 and it changes at a rate of 15% per annum. The number of students during 2015.
  • a)
    Quantity I > Quantity II
  • b)
    Quantity I < quantity="" />
  • c)
    Quantity I = Quantity II or the relationship cannot be determined
  • d)
    Quantity I ≥ Quantity II
  • e)
    Quantity I ≤ Quantity II
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
In the following questions, two statements numbered I and II are give...
Quantity I
CI = 150000 x (1.12)3 - 150000 = 210739.2 - 150000 = 60739.2
SI = 150000 x 12 x 3/100 = 54000
Difference = Rs 6739.2
Quantity II:
Since the nature of change is not given, the number of students may increase or decrease.
Case 1: when there is increase
Number in 2015 = 5600 x 1.15 x 1.15 = 7406
Case 2: when there is decrease
Number in 2015 = 5600 x 0.85 x 0.85 = 4046
Hence, Relation can't be established.
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Community Answer
In the following questions, two statements numbered I and II are give...
Understanding Quantity I: Difference between CI and SI
To calculate the difference between Compound Interest (CI) and Simple Interest (SI) for a principal amount of 150,000 at a rate of 12% per annum over 3 years:
- Simple Interest Formula:
SI = P * r * t
- P = 150,000
- r = 12/100 = 0.12
- t = 3
- SI = 150,000 * 0.12 * 3 = 54,000
- Compound Interest Formula:
CI = P * (1 + r)^t - P
- CI = 150,000 * (1 + 0.12)^3 - 150,000
- CI = 150,000 * (1.404928) - 150,000 = 60,739.20
- Difference = CI - SI = 60,739.20 - 54,000 = 6,739.20
Thus, Quantity I = 6,739.20.
Understanding Quantity II: Number of Students in Navodaya Vidyalaya
To find the number of students in 2015 given the number in 2013 was 5,600 with a growth rate of 15% per annum:
- Student Calculation:
- Number of students in 2014 = 5600 * (1 + 0.15) = 5600 * 1.15 = 6440
- Number of students in 2015 = 6440 * 1.15 = 7406
Thus, Quantity II = 7,406.
Comparing Quantities
- Quantity I = 6,739.20
- Quantity II = 7,406
Since Quantity I is less than Quantity II, we conclude:
Correct Answer
- Option C: Quantity I < quantity="" ii="" or="" the="" relationship="" cannot="" be="" determined.="" quantity="" ii="" or="" the="" relationship="" cannot="" be="" />
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