Math, asked by gopalbhople20, 2 months ago

Age of Lata is AB and age of Asha is CD. If the digits of their ages are arranged as ABCD then the 4 digit number thus formed is a perfect square of a paticular number.If the same operation is repeated after 11 years then the 4 digit so formed is also a perfect square number of another number.Find the present ages of Asha and Lata.
(Value of A and B may be different)​

Answers

Answered by shindesudhakar695
0

Answer:

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Step-by-step explanation:

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Answered by RvChaudharY50
1

Answer :-

Let present age of Lata is (10A + B) and present age of Asha is (10C + D) .

Case 1) :- ABCD is square . Let it a square of number x .

so,

→ 1000A + 100B + 10C + D = x² -------- Eqn.(1)

Case 2) :- 11 years later .

→ Lata will be = (10A + B) + 10 + 1 = 10(A + 1) + (B + 1)

→ Asha will be = (10C + D) + 10 + 1 = 10(C + 1) + (D + 1)

again, it a perfect square of let y .

so,

→ 1000(A + 1) + 100(B + 1) + 10(C + 1) + (D + 1) = y²

→ 1000A + 1000 + 100B + 100 + 10C + 10 + D + 1 = y²

→ 1000A + 100B + 10C + D + 1111 = y²

putting value of Eqn.(1),

→ x² + 1111 = y²

→ y² - x² = 1111

→ (y + x)(y - x) = 1111

→ (y + x)(y - x) = 101 * 11

then,

→ y + x = 101 --------- Eqn.(2)

→ y - x = 11 --------- Eqn.(3)

adding Eqn.(2) and Eqn.(3)

→ y + x + y - x = 112

→ 2y = 112

→ y = 56

putting value of y in Eqn.(3),

→ 56 - x = 11

→ x = 56 - 11

→ x = 45

therefore,

  • ABCD = x² = 45² = 2025
  • ABCD = y² = 56² = 3136
  • 20 + 11 = 31 and 25 + 11 = 36 .

Hence, the present ages of Asha(AB) is 20 years and Present age of Lata(CD) is 25 years.

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