A two digit number is four times the sum of the two digits. If the digits are reversed, the number so obtained is 18 more than the original number. What is the original number? (Number Concept)

Shohan

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2025-01-04 04:42

1 Answers

Shohan

প্রশ্নে বলা হচ্ছে, দুই অঙ্ক বিশিষ্ট কোন সংখ্যা তার অঙ্ক দুটির যোগফলের 4 গুণ। অঙ্ক দুটিকে স্থান পরিবর্তন করলে যে সংখ্যা পাওয়া যায় তা মূল সংখ্যার চেয়ে 18 বেশি। মূল সংখ্যাটি কত?

Let, Tenth digit is x and unit digit is y

∴ The number = (10x + y)

According to first condition, $4 (x + y) = 10 x + y . . . . . . . . . . . . (i)$

And second condition, $(10 x + y) + 18 = 10 y + x . . . . . . . . . . . . . (i i)$

From equation (ii), $10 x + y + 18 = 10 y + x$

$\Rightarrow 9 x - 9 y = - 18 \Rightarrow 9 y - 9 x = 18 [M u l t i p l y i n g b y - 1] \Rightarrow 9 (y - x) = 18 \Rightarrow (y - x) = \frac{18}{9} = 2 \Rightarrow y - x = 2 ∴ y = x + 2 . . . . . . . . . (i i i)$

From equation (i), we get $4 (x + y) = 10 x + y$

$\Rightarrow 4 x + 4 y = 10 x + y \Rightarrow 3 y = 6 x \Rightarrow y = 2 x \Rightarrow x + 2 = 2 x [P u t t i n g t h e v a l u e o f y] ∴ x = 2$

Now, putting the value of x in equation (iii) we get

$y = x + 2 \Rightarrow y = 2 + 2 = 4 ∴ y = 4 T h e n u m b e r i s (10 x + y) = (10 \times 2) + 4 = 20 + 4 = 24 . a n s .$

5 views Answered 2024-12-14 13:31

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