(English Medium) ICSE Class 10 - CISCE Question Bank Solutions

In the given figure, PQ is a tangent to the circle at A. AB and AD are bisectors of ∠CAQ and ∠PAC. if ∠BAQ = 30°. Prove that:

1. BD is a diameter of the circle.
2. ABC is an isosceles triangle.

If (3a + 2b) : (5a + 3b) = 18 : 29. Find a : b

A page from the savings bank account of Mrs Ravi is given below.

She closed the account on 30th September 2006. Calculate the interest Mrs Ravi earned
at the end of 30th September 2006 at 4.5% per annum interest. Hence, find the
amount she receives on closing the account.

Draw a line AB = 5 cm. Mark a point C on AB such that AC = 3 cm. Using a ruler and a compass only, construct:

1. A circle of radius 2.5 cm, passing through A and C.
2. Construct two tangents to the circle from the external point B. Measure and record the length of the tangents.

Mohan has a recurring deposit account in a bank for 2 years at 6% p.a. simple interest. If he gets Rs. 1200 as interest at the time of maturity, find:

1. the monthly instalment.
2. the amount of maturity.

Sonia had a recurring deposit account in a bank and deposited Rs. 600 per month for 2 1/2 years. If the rate of interest was 10% p.a., find the maturity value of this account.

The 4th term of a G.P. is 16 and the 7th term is 128. Find the first term and common ratio of the series

In the figure given below, O is the centre of the circle and SP is a tangent. If ∠SRT = 65°,
find the value of x, y and z.

Virat opened a Savings Bank account in a bank on 16th April 2010. His pass book shows the following entries:

Calculate the interest Virat earned at the end of 31st July 2010 at 4% per annum interest. What sum of money will he receive if he closed the account on 1st August 2010?

If a, b, c are in continued proportion, prove that (a + b + c) (a – b + c) = a² + b² + c²

Shahrukh opened a ‘Recurring Deposit’ account in a bank and deposited Rs. 800 per month for 1½ years. If he received Rs. 15,084 at the time of maturity, find the rate of interest per annum.

Calculate the ratio in which the line joining A(−4, 2) and B(3, 6) is divided by point P(x, 3). Also, find

1. x
2. length of AP.

A shopkeeper bought a washing machine at a discount of 20% from a wholesaler, the printed price of the washing machine being Rs. 18,000. The shopkeeper sells it to a consumer at a discount of 10% on the printed price. If the rate of sales tax is 8%, find:
(i) the VAT paid by the shopkeeper.
(ii) the total amount that the consumer pays for the washing machine

In the figure given below, diameter AB and chord CD of a circle meet at P. PT is a tangent to the circle at T. CD = 7.8 cm, PD = 5 cm, PB = 4 cm. Find: 

1) AB.

2) the length of tangent PT.

If (x - 9) : (3x + 6) is the duplicate ratio of 4: 9, find the value of x.

A page from the ‘Savings Bank’ account of Priyanka is given below:

If the interest earned by Priyanka for the period ending September 2006 is Rs. 175, the find the rate of interest.

At what rate % p.a. will a sum of Rs. 4000 yield Rs. 1324 as compound interest in 3 years?

The monthly pocket money of Ravi and Sanjeev are in the ratio 5 : 7. Their expenditures are in the ratio 3 : 5. If each saves Rs. 80 every month, find their monthly pocket money.

On what sum of money will the difference between the compound interest and simple interest for 2 years be equal to Rs. 25 if the rate of interest charged for both is 5% p.a.?

A page from the Savings Bank Account of Mr Prateek is given below:

If he receives Rs. 198 as interest on 1st January 2007, find the rate of interest paid by the bank.