Question
Rs. βPβ 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 βTβ 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 βTβ is an even number. (2) The value of βPβ is the multiple of 6. (3) (P/12)-5T = 3303Solution
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. βPβ 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 βTβ 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 βPβ 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 βTβ is an even number. The above given statement is true. (2) The value of βPβ 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.
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