Mr. Mohan divided a sum of money into three parts 5^x , 3^y and 2^z and distributed among his three sons Aman, Aryan and Asmit respectively. The product of their share is 12,96,000.
(i) Find the share of Aman.
(ii) Find the sum of shares of Aryan and Asmit.
(iii) Find the value of (x + y + z).
(iv) Find the value of $\Big(\sqrt{x^y}\Big)^{z - 5}$

Question

Mr. Mohan divided a sum of money into three parts 5^x , 3^y and 2^z and distributed among his three sons Aman, Aryan and Asmit respectively. The product of their share is 12,96,000.
(i) Find the share of Aman.
(ii) Find the sum of shares of Aryan and Asmit.
(iii) Find the value of (x + y + z).
(iv) Find the value of $\Big(\sqrt{x^y}\Big)^{z - 5}$

KnowledgeBoat · Accepted Answer

Given, Shares are : Aman = 5x Aryan = 3y Asmit = 2z Product of shares = 12,96,000. 5x × 3y × 2z = 12,96,000 By prime factorization, 1296000 = 27 × 34 × 53 Comparing the powers, 5x. 3y. 2z = 53. 34. 27 ∴ x = 3, y = 4, z = 7 (i) Share of Aman, 5x = 53 = 125. Hence, share of Aman = 125. (ii) Sum of Aryan and Asmit, 3y + 2z = 34 + 27 = 81 + 128 = 209. Hence, sum of shares of Aryan and Asmit = 209. (iii) (x + y + z) = (3 + 4 + 7) = 14. Hence, x + y + z = 14. (iv) Calculating, Hence, = 81.

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