Answered

1. Sangita has deposited Rs. [tex]$1,00,000$[/tex] in a commercial bank for 2 years at the rate of Rs. 5 interest per annum for Rs. 100.

a. At what percent interest rate per annum had Sangita deposited the amount of money?

b. How much interest will Sangita get in 2 years at the same rate of interest?

c. The ages of Sangita's elder and younger daughters are 12 years and 8 years, respectively. If Sangita divides her Rs. [tex]$1,00,000$[/tex] between her daughters based on the ratio of their ages, how much more money will the elder daughter get than the younger daughter?



Answer :

GinnyAnswer
Sure, let's address each part of the question step-by-step.

### Part (a)

Question:
At what percent of interest rate per annum had Sangita deposited the amount of money?

Solution:
The interest rate per annum provided is Rs 5 for every Rs 100.

To convert this into a percentage:
[tex]\[ \text{Interest rate per annum} = \left(\frac{5}{100}\right) \times 100\% = 5\% \][/tex]

So, Sangita had deposited the amount at a 5% interest rate per annum.

### Part (b)

Question:
How much interest will Sangita get in 2 years at the same rate of interest?

Solution:
To calculate the total interest earned on the deposit, we can use the simple interest formula:
[tex]\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \][/tex]

Given data:
- Principal (P) = Rs 1,00,000
- Rate (R) = 5% per annum
- Time (T) = 2 years

Break it down:
[tex]\[ R = 5\% \text{ per annum} = \frac{5}{100} = 0.05 \][/tex]

[tex]\[ \text{Interest for 1 year} = 1,00,000 \times 0.05 = 5,000 \][/tex]

[tex]\[ \text{Interest for 2 years} = 5,000 \times 2 = 10,000 \][/tex]

Therefore, Sangita will get Rs 10,000 as interest in 2 years.

### Part (c)

Question:
The ages of elder and younger daughters of Sangita are 12 years and 8 years respectively. If Sangita divides her Rs 1,00,000 to her daughters based on the ratio of their ages, how much more money will the elder daughter get than the younger daughter?

Solution:
First, find the total ratio based on ages:
- Age of elder daughter = 12 years
- Age of younger daughter = 8 years

Total ratio = 12 (elder daughter's age) + 8 (younger daughter's age) = 20

Now, calculate each daughter's share of the Rs 1,00,000 based on this ratio.

[tex]\[ \text{Elder daughter's share} = \left(\frac{12}{20}\right) \times 1,00,000 = 60,000 \][/tex]

[tex]\[ \text{Younger daughter's share} = \left(\frac{8}{20}\right) \times 1,00,000 = 40,000 \][/tex]

Now, to find out how much more the elder daughter gets than the younger daughter:
[tex]\[ \text{Difference} = 60,000 - 40,000 = 20,000 \][/tex]

So, the elder daughter will get Rs 20,000 more than the younger daughter.
chibabykalu16

Answer:

a) 5%

b) Rs. 10000

c) Rs. 20000

Step-by-step explanation:

Given:

  • Principal Amount (P) = Rs. 1,00,000
  • Interest per annum for Rs. 100 = Rs. 5

a)

The interest rate for Rs. 100 is Rs. 5, which means the interest rate is 5%.

Based on:  [tex]\text{Interest Rate $(\%)$} = \frac{5}{100} \times 100 = 5\%[/tex]

b)

[tex]\text{Interest} = \frac{\text{Principal $\times$ Time $\times$ Rate }}{100}[/tex]

Where:

  • The Principal is equal to 100000
  • Time is 2 years
  • Rate = 5%

[tex]\text{Interest} = \frac{\text{100000 $\times$ 2 $\times$ 5 }}{100}[/tex]

[tex]\text{Interest} = \text{1000 $\times$ 2 $\times$ 5 }[/tex]

[tex]\text{Interest} = \text{Rs.10000}[/tex]

c)

To find out how much more money the elder daughter will get than the younger daughter, we need to divide the total amount of Rs. 1,00,000 between the daughters based on the ratio of their ages.

[tex]\text{Ratios} = \frac{12}{8} = \frac{3}{2}[/tex]

3x would represent the elder daughter (12 years) and 2x would represent the younger daughter (8 years)

3x + 2x = 100000

5x = 100000

x = 100000/5

x = 20000

For the elder daughter = 3x = 3(20,000) = 60,000

For the younger daughter = 2x = 2(20,000) = 40,000

Difference = 60,000 - 40,000 = Rs. 20,000

Therefore, the elder daughter would receive Rs. 20,000 more than the younger daughter

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