Rs. ‘P’ was invested in scheme A at the rate of 30% per annum on compound interest for 3 years. Rs. (P+9875) was invested in scheme B at the rate of 24% per annum on simple interest for ‘T’ years. The interest obtained from both of the schemes (A and B) is the same. If Rs. (P-2000) was invested in scheme C at the rate of 25% per annum on simple interest, then after 6 years Rs. 57000 was obtained as an interest.

Which of the following statements is/are true?

(1) The value of ‘T’ is an even number.

(2) The value of ‘P’ is the multiple of 6.

(3) (P/12)-5T = 3303

Solution

If Rs. (P-2000) was invested in scheme C at the rate of 25% per annum on simple interest, then after 6 years Rs. 57000 was obtained as an interest. (P-2000)x25%x6 = 57000 (P-2000)x150% = 57000 1.5(P-2000) = 57000 (P-2000) = 38000 P = 38000+2000 P = 40000 Rs. ‘P’ was invested in scheme A at the rate of 30% per annum on compound interest for 3 years. Rs. (P+9875) was invested in scheme B at the rate of 24% per annum on simple interest for ‘T’ years. The interest obtained from both of the schemes is the same. P x (100+30)% x (100+30)% x (100+30)% - P = (P+9875) x 24% x T P x 130% x 130% x 130% - P = (P+9875) x 24% x T Put the value of ‘P’ in the above equation. 40000 x 1.3 x 1.3 x 1.3 - 40000 = (40000+9875) x 24% x T 40000 x 1.3 x 1.3 x 1.3 - 40000 = 49875 x 24% x T 40000x(1.3 x 1.3 x 1.3 - 1) = 11970 x T 40000x(2.197 - 1) = 11970 x T 40000x1.197 = 11970 x T 11970T = 47880 T = 4 (1) The value of ‘T’ is an even number. The above given statement is true. (2) The value of ‘P’ is the multiple of 6. The above given statement is not true. (3) (P/12)-5T = 3303 (40000/12)-5x4 = 3303 (10000/3)-20 = 3303 (10000-60)/3 = 3303 9940/3 = 3303 The above given statement is not true. Because the given equation is not satisfied.