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
Answer:
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Step-by-step explanation:
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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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