​ On a certain amount at 12 (1/2)% rate for 1 years it becomes ₹ 2437.50 then the amount is ………………..  ​

Correct option is  B) 15 years

Correct option is (D) none Let Ramu's present age be x years. \(\therefore\) Ramu's age before 4 years = (x - 4) years Ramu's age after 12 years = (x + 12) years \(\therefore\) x+12 = 3(x-4) \(\Rightarrow\) x+12...

Correct option is  D) ₹ 7,100

Correct option is (A) 8 Let the amount taken be Rs P. \(\therefore\) S.I. = \(\frac{16}{25}\times\) P = \(\frac{16P}{25}\) R = T \(\therefore\) S.I. = \(\frac{PRT}{100}\) \(\Rightarrow\) \(\frac{16P}{25}\) = \(\frac{P\times R\times R}{100}\)  \((\because\)  R = T) \(\Rightarrow\) \(R^2=\) \(\frac{16P}{25}\times\frac{100}P\) \(=16\times4=64=8^2\) \(\Rightarrow\) R = 8 \(\Rightarrow\) T = R = 8

Correct option is (C) ₹ 2166.66 Let the amount be P. R = \(12\frac{1}{2}\%=\frac{25}{2}\%\) T = 1 year Amount after 1 year \(=P(1+\frac R{100})^1\) \(\Rightarrow\) \(P(1+\frac R{100})\) = 2437.50   (Given) \(\Rightarrow\) \(P(1+\frac{25}{200})\) = 2437.50 \(\Rightarrow\) \(P(1+\frac18)\) = 2437.50 \(\Rightarrow\) \(\frac{9P}8\) = 2437.50 \(\Rightarrow\) P = 2437.50 \(\times\frac89=\frac{19500}9\) = 2166.66 \(\therefore\) Amount is Rs 2166.66

Correct option is (A) ₹ 3375 Let the amount be Rs x. R = 12% T = 3 years Amount after 3 years = Rs 4590 \(\therefore\) \(x+\frac{x\times12\times3}{100}\) = 4590   (Amount after 3 years \(=P+\frac{PRT}{100})\) \(\Rightarrow\) \(x+\frac{9x}{25}\) = 4590 \(\Rightarrow\) \(\frac{34x}{25}\) = 4590 \(\Rightarrow\) \(x=\frac{4590\times25}{34}\) = 3375

Let the present age of Shikha be ‘a’ years.  Given, product of Shikha’s age five years ago and her age 8 years later is 30  ⇒ (a – 5)(a + 8) =...