High School

66. A man invested Rs. X in a scheme offering 20% p.a. at CI compounding annually for 2 years. If the interest received by the man for only the second year is Rs. 4,800, then find X.

1. Rs. 20,000
2. Rs. 15,000
3. Rs. 25,000
4. Rs. 30,000
5. Rs. 10,000

67. The average of five consecutive numbers is 17. What will be the average of the largest and second smallest number out of these five numbers?

1. 17
2. 17.5
3. 16
4. 18.5
5. 18

68. A 300 m long train crosses a bridge in 54 seconds, and the length of the bridge is twice that of the train. Find the speed of the train.

1. 1.60 km/h
2. 2.55 km/h
3. 3.65 km/h

Answer :

Let's tackle each of these questions step-by-step:

  1. Question about Compound Interest:

Given:

  • Compound Interest (CI) rate = 20% per annum
  • Interest received in just the second year = Rs. 4,800

We need to find the principal amount (X).

The compound interest formula for the amount at the end of the second year is:
[tex]A = X (1 + r)^2[/tex]
where [tex]r = \frac{20}{100} = 0.2[/tex].

The interest received in the second year should be:
[tex]\text{Interest for 2nd year} = A_{2} - A_{1}[/tex]
where [tex]A_{2}[/tex] is the amount at the end of year 2, and [tex]A_{1}[/tex] is the amount at the end of year 1.

We know:[tex]A_{2} = X (1.2)^2[/tex]
[tex]A_{1} = X (1.2)[/tex]

Thus,
[tex]\text{Interest for 2nd year} = X (1.2)^2 - X(1.2) = 4,800[/tex]
[tex]X (1.44 - 1.2) = 4,800[/tex]
[tex]X (0.24) = 4,800[/tex]
[tex]X = \frac{4,800}{0.24}[/tex]
[tex]X = 20,000[/tex]

So, the answer is Option 1: Rs. 20,000.

  1. Average of Consecutive Numbers:

Given:

  • The average of five consecutive numbers is 17.

We need to find the average of the largest and the second smallest numbers.

Let's represent the five consecutive numbers as [tex]n-2, n-1, n, n+1, n+2[/tex].

The average of these numbers is:
[tex]\frac{(n-2) + (n-1) + n + (n+1) + (n+2)}{5} = 17[/tex]
[tex]\frac{5n}{5} = 17[/tex]
[tex]n = 17[/tex]

The numbers are 15, 16, 17, 18, and 19.

  • The largest number = 19
  • The second smallest number = 16

The average of these two numbers is:
[tex]\frac{19+16}{2} = \frac{35}{2} = 17.5[/tex]

So, the answer is Option 2: 17.5.

  1. Train Crossing a Bridge:

Given:

  • Length of the train = 300 m
  • Length of the bridge = 2 × length of the train = 2 × 300 = 600 m
  • Total length to be crossed = 300 m (train length) + 600 m (bridge length) = 900 m
  • Time taken to cross = 54 seconds

We need to find the speed of the train.

First, calculate the speed in meters per second (m/s):
[tex]\text{Speed} = \frac{\text{Total Length}}{\text{Time}} = \frac{900 \text{ m}}{54 \text{ s}} = 16.67 \text{ m/s}[/tex]

Convert this to kilometers per hour (km/h):
[tex]\text{Speed in km/h} = 16.67 \times \frac{18}{5} = 60 \text{ km/h}[/tex]

Therefore, the speed of the train is 60 km/h.

None of the provided options in the question matches, so there might be an error in the options given. The correct speed is 60 km/h.

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