Q. 61. A mobile-phone can be purchased for Rs. 28,000 cash or for Rs. 7400 cash down payment followed by four equal monthly instalements of Rs. 5200 each. Find the rate of interest charged under the instalement plan.
Q. 62. A video camera is sold for Rs. 5600 cash or for Rs. 1800 cash down payment and 10 equal monthly instalements of Rs. 400 each. Find the rate of interest charged.
Q. 63. A house is sold for Rs. 4,50,000 cash or for Rs. 1,50,000 cash down payment followed by 10 equal monthly instalements of Rs. 32000 each. Find the rate of interest.
Q. 64. Hamish borrowed a sum of money and returned it in three equal quarterly instalements of Rs. 17576 each. If the rate of interest charged was 16% per annum; find the total interest paid by him.
Q. 65. A loan of Rs 12750 is to be paid back in two equal half yearly instalements. If the interest is compounded half yearly at 8% per annum, how much is each instalement.
Q. 66. A room heater is sold for Rs. 1320 cash or for Rs. 600 cash down payment together with Rs. 732 to be paid after one month. Find the rate of interest charged under the instalement plan.
Q. 67. A car is available for Rs. 4, 02, 200 cash or for Rs. 1, 50, 000 cash down payment and 3 equal half yearly instalements. If the interest is charged at 10% per annum compounded half yearly, find the value of each instalement.
Q. 68. A loan of Rs. 17, 200 is to be returned in two equal annual instalements. If the rate of interest charged is 15% per annum compounded annually, find the amount of each instalement.
Q. 69. A dressing-table can be purchased for Rs. 9, 700 cash or for Rs. 2, 100 cash down payment followed by three equal monthly instalements of Rs. 2, 600 each. Find the rate of interest charged.
Q. 70. An mp3 player can be purchased for Rs. 1, 500 cash or for Rs. 360 cash down payment followed by three equal monthly instalements . If the rate of interest charged is 16% per annum, find the monthly instalement.
Q. 71. Kartika’s monthly income is Rs. 25, 000. She contributes Rs. 20 ,000 towards GPF and invests Rs. 20, 000 in NSC’s. She donates Rs. 5, 100 to a medical research centre, thus getting a relief of 100% on the donation. Compute her income tax.
Q. 72. Ankur is a senior citizen aged 71 years. He works in a private firm and gets a monthly salary of Rs. 22, 000. He contributes Rs. 45, 000 towards PPF and donates Rs. 3, 100 towards P.M.’s National Relief Fund. Compute his income tax.
Q. 73. The annual income of Kapil is Rs. 2, 80, 000. He contributes Rs. 4, 500 per month in Provident Fund and pays Rs. 8, 000 annually towards LIC premium. Find the income tax to be paid by Kapil in the last month of the year if he paid Rs. 1, 500 per month as income tax for the first 11 months.
Q. 74. Ramesh has an annual income of Rs. 5, 10, 000. He pays an annual LIC premium of Rs. 20, 000 and invests Rs. 20, 000 in National Saving Certificates and contributes Rs. 5, 000 per month to his Provident Fund. He pays Rs. 6, 000 per month for 11 months as income tax. Find the income tax to be paid by him in the last month of the year.
Q. 75. Dr. Salim is a senior citizen and earns Rs. 28, 000 per month. He donates Rs. 6, 000 to PMRF (100% relief) and Rs. 4, 000 to an institution (50 % relief). He contributes Rs. 60, 000 towards PPF and purchases NSC’s worth Rs. 15, 000. He pays Rs. 900 per month for the first 11 months of the year. Find the income tax to be paid by him in the last month of the year.
Q. 76. Amit’s monthly salary is Rs. 19,250. He contributes Rs. 2,500 per month towards GPF and Rs. 20, 000 towards PPF. He donates Rs. 11, 000 to a school and gets a relief of 50% on the donation. Calculate the income tax deducted from his salary in the last month of the year, if the tax deduction is made from his salary for 11 months at the rate of Rs. 800 per month.
Q. 77. The annual income of Ravish is Rs. 2,80, 000. He donates Rs. 5, 000 to PMRF. He contributes Rs. 5, 000 per month in his provident fund and pays an annual insurance premium of Rs. 15,000. Calculate his income tax for the financial year.
Q. 78. Rahul aged 67 years, gets a pension of Rs. 25, 000 per month. He contributes Rs. 40,000 towards PPF and purchases NSC worth Rs. 20, 000. He also donates Rs. 10, 000 towards PMRF. Calculate the income tax to be paid by him in the last month of the year, if his earlier deductions as income tax, for the first 11 months were at the rate of Rs. 800 per month.
Q. 79. The monthly income of Anita is Rs 30, 000. She donates Rs. 8, 400 towards PMRF and Rs. 12, 000 to an orphanage. She contributes Rs. 4,500 per month towards Provident Fund and Rs. 2,500 per quarter as LIC premium. She purchases NSC’s worth Rs. 10,000. She pays Rs. 2, 500 per month as income tax for the first 11 months of the year. Calculate her income tax for the last month of the year.
Q. 80. Radha’s annual salary is Rs. 1, 65, 000. She contributes Rs. 10, 000 towards GPF and pays an annual LIC premium of Rs. 10, 000. Calculate the income tax to be paid by her for the financial year.
Q. 81. Two sides and a median bisecting one of these sides of a triangle are respectively proportional to the two sides and the corresponding median of the other triangle. Prove that the two triangles are similar.
Q. 82. In a triangle ABC, AD is perpendicular to the side BC and if BD/DA = DA/DC, prove that ABC is a right triangle.
Q. 83. ABC is a right triangle right-angled at B and the side BC is trisected at the points D and E such that the points B,D,E,C are in continuous manner. Prove that: 8 AE2 = 3 AC2 + 5 AD2.
Q. 84. Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.
Q. 85. The perpendicular from A to the side BC of a ∆ ABC intersects the side BC at D such that DB = 3 CD. Prove that: 2 AB2 = 2 AC2 + BC2.
Q. 86. In a triangle ABC, DE // BC, BD : AB = 3:7. Find the ratio of the areas of the triangles ADE and ABC.
Q. 87. If one diagonal of a trapezium divides the other diagonal in the ratio 1:2, prove one of its parallel sides is double the other.
Q. 88. ABC is a triangle in which AB = AC and D is a point on AC such that BC2 = AC × CD. Prove that ∆BCD is isosceles.
Q. 89. Through the mid-point M of the side CD of a parallelogram ABCD, the line BM is drawn intersecting AC in L and AD produced in E. Prove that: EL = 2 BL.
Q. 90. ABC is a triangle in which AB = AC and D is any point on side BC. Prove that: AB2 - AD2 = BD × CD.
