(English Medium) ICSE Class 9 - CISCE Question Bank Solutions for Mathematics

Prove the following: `(tan(90° - θ)cotθ)/("cosec"^2 θ)` = cos²θ

Prove the following: sin²30° + cos²30° = `(1)/(2)sec60°`

If A + B = 90°, prove that `(tan"A" tan"B" + tan"A" cot"B")/(sin"A" sec"B") - (sin^2"B")/(cos^2"A")` = tan²A

Find the value of 'a' and 'b' if
a. (a + 2,5 + b) = (1, 6)
b. (2a + b, a - 2b) = (7, 6)

Each of the equal sides of an isosceles triangle is 4 cm greater than its height. If the base of the triangle is 24 cm; calculate the perimeter and the area of the triangle.

A sum is invested at compound interest, compounded yearly. If the interest for two successive years is Rs. 5,700 and Rs. 7,410. calculate the rate of interest.

A certain sum of money is put at compound interest, compounded half-yearly. If the interest for two successive half-years are Rs. 650 and Rs. 760.50; find the rate of interest.

A certain sum amounts to Rs. 5,292 in two years and Rs. 5,556.60 in three years, interest being compounded annually. Find : the rate of interest.

A certain sum amounts to Rs. 5,292 in two years and Rs. 5,556.60 in three years, interest being compounded annually. Find: the original sum.

The compound interest, calculated yearly, on a certain sum of money for the second year is Rs. 1,089 and for the third year it is Rs. 1,197.90. Calculate the rate of interest and the sum of money.

Mohit invests Rs. 8,000 for 3 years at a certain rate of interest, compounded annually. At the end of one year it amounts to Rs. 9,440. Calculate: 

1. the rate of interest per annum.
2. the amount at the end of the second year.
3. the interest accrued in the third year.

Geeta borrowed Rs. 15,000 for 18 months at a certain rate of interest compounded semi-annually. If at the end of six months it amounted to Rs. 15,600; calculate :
(i) the rate of interest per annum.
(ii) the total amount of money that Geeta must pay at the end of 18 months in order to clear the account.

Ramesh invests Rs. 12,800 for three years at the rate of 10% per annum compound interest. Find:

1. the sum due to Ramesh at the end of the first year.
2. the interest he earns for the second year.
3. the total amount due to him at the end of the third year.

Rs. 8,000 is lent out at 7% compound interest for 2 years. At the end of the first year Rs. 3,560 are returned. Calculate :
(i) the interest paid for the second year.
(ii) the total interest paid in two years.
(iii) the total amount of money paid in two years to clear the debt.

The cost of a machine depreciated by Rs. 4,000 during the first year and by Rs. 3,600 during the second year. Calculate :

1. The rate of depreciation.
2. The original cost of the machine.
3. Its cost at the end of the third year.

Find the sum, invested at 10% compounded annually, on which the interest for the third year exceeds the interest of the first year by Rs. 252.

A man borrows Rs.10,000 at 10% compound interest compounded yearly. At the end of each year, he pays back 30% of the sum borrowed. How much money is left unpaid just after the second year ?

A man borrows Rs.10,000 at 10% compound interest compounded yearly. At the end of each year, he pays back 20% of the amount for that year. How much money is left unpaid just after the second year ?

What sum will amount of Rs. 6,593.40 in 2 years at C.I. , if the rates are 10 per cent and 11 per cent for the two successive years ?

The value of a machine depreciated by 10% per year during the first two years and 15% per year during the third year. Express the total depreciation of the machine, as percent, during the three years.