Home
Class 10
MATHS
If the simple interest of a certain sum ...

If the simple interest of a certain sum of money for 1 year is Rs. 50 and compound interest for 2 years is Rs. 102, then find the sum of money and the rate of interest.

Text Solution

Verified by Experts

Let the principal be Rs. `x` and the rate of interest be r% per annum.
`:.` at the rate of r% interest per annum, the
simple interest of 1 year `=Rs. (x xxr xx1)/100=Rs. (rx)/100`
As per question `(rx)/100=50impliesrx=5000`…………..1
Again at the rate of r% compound interest per annum of Rs. x in 2 years,
the amount `=Rs. x xx(1+r/100)^(2)`
`:.` The compound interest `=Rs.{x xx(1+r/1-100)^(2)-x}`
`=Rx[(1+r/100)^(2)-1]`
`=Rs. x[(1+r/100+1)(1+r/100-1)]`
`=Rs. x[(2+r/100)xxr/100]`
`=Rs. (xr)/100(2+r/100)`
`Rs. 5000/100(2+r/100)` [by 1]
`=Rs. 50(2+r/100)=Rs. (100+r/2)`
As per question `100+r/2=102-100impliesr/2=2impliesr=4`
`:.` From 1 we get `4x=5000[ :'r=4]`
`impliesx=5000/rimpliesx=1250`
`:.` The required sum of money `=Rs. 1250` and rate of interest `=4%` per annum.
Promotional Banner

Topper's Solved these Questions

  • COMPOUND INTEREST

    CALCUTTA BOOK HOUSE|Exercise MCQ TYPE|10 Videos

  • COMPOUND INTEREST

    CALCUTTA BOOK HOUSE|Exercise VERY SHORT ANSWER QUESTION TYPE|5 Videos

  • APPLICATION OF TRIGONOMETRIC RATIOS: HEIGHTS AND DISTANCES

    CALCUTTA BOOK HOUSE|Exercise (Long-answer type question (LA) :)|11 Videos

  • CONCEPT OF MEASUREMENT OF ANGLES

    CALCUTTA BOOK HOUSE|Exercise EXERCISE - 1|38 Videos

Similar Questions

Explore conceptually related problems

If simple interest and compound interest of a certain sum of money for two years are Rs. 8400 and Rs. 8652 respectively, then find the sum of money and the rate of interest.

The simple interest and compound interest of a certain sum of mone for 2 years are Rs. 840 and Rs. 869.40 respectively. Find the sum of money and the rate of interest.

If simple interest and compound interest of a certain sum of money for two years are Rs 8400 and Rs 8652 respectively, then calculate the sum of money and rate of interest.

If the compound interest of some money for 2 years at the rate of compound interest 5% per annum is Rs 615, then find the invested money.

The simnple interest and compound interest on a certain sum os money for 2 years in Rs. 840 and Rs 869.40 respectively Find the sum and the annual rate of interest.

If the simple interest on a sum at 4% per annum for 2 years is Rs. 80, then the compound interest on the same sum for the same period is?

The simple interest on a sum of money for 2 years at 4% per annum is Rs. 340.Find the sum of money?

State whether the following statement is true or false: I. The compound interest of a certain sum of money for a certain period of time at the certain rate of compound interest per annum is less than the simple interest of the same sum of money for the same period of time and at the same rate of interest. II. In the case of compound interest the quantity of principal gradually increases. III. In the case of compound interest, the rate of interest changes every year. IV. In the case of compound interest, the same quantity of interest is obtained in every year. V. In the case of compound interest the obtained interest is proportional to the period of time.

If the compound interests in two consecutive years be Rs. 400 and Rs. 432 then the rate of interest is

If the amount of Rs 100 for 2 years is Rs 121, then find the rate of compound interest in percent per annum.