The sum of the first two digits of a three digit number is equal to the third digit. If the digits are reversed, the number so obtained is 198 more than the original number. What are the possible original numbers?

Created: 2 months ago | Updated: 2 months ago

Job Solution Combined Bank (সমন্বিত ব্যাংক) Combined 7 Banks & Financial Institutions || Senior Officer (19-11-2021) || 2021 গণিত

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$L e t, x b e t h e 100 t h d i g i t; y b e t h e 10 t h d i g i t a n d z b e t h e u n i t d i g i t$

$∴ T h e n u m b e r i s = (100 x + 10 y + z) A c c o r d i n g q u e s t i o n t o, (x + y) = z . . . . . . . (i)$

$(100 x + 10 y + z) = x + 10 y + 100 z - 198 = x - 100 x + 10 y - 10 y + 100 z - z = 198 = 99 z - 99 x = 198 = 99 (z - x) = 198 = (z - x) = \frac{198}{99} = 2$

$= x + y - x = 2 [P u t t i n g z = x + y] ∴ y = 2 [H e r e, 10 t h d i g i t a l w a y s w i l l b e 2] W h e n x = 1 t h e n t h e p o s s i b l e n u m b e r i s = 1 + 2 = 3 : h e r e b y t h e n u m b e r i s 123 . ∴ x = 2 t h e n t h e p o s s i b l e n u m b e r i s 2 + 2 = 4; h e r e b y t h e n u m b e r i s 224 . ∴ x = 3 t h e n t h e p o s s i b l e n u m b e r i s = 3 + 2 = 5; h e r e b y t h e n u m b e r i s 325 . ∴ x = 4 t h e n t h e p o s s i b l e n u m b e r i s = 4 + 2 = 6 : h e r e b y t h e n u m b e r i s 426 . ∴ x = 5 t h e n t h e p o s s i b l e n u m b e r i s = 5 + 2 = 7; h e r e b y t h e n u m b e r i s 527 . ∴ x = 6 t h e n t h e p o s s i b l e n u m b e r i s = 6 + 2 = 8; h e r e b y t h e n u m b e r i s 62 . ∴ x = 7 t h e n t h e p o s s i b l e n u m b e r i s = 7 + 2 = 9 : h e r e b y t h e n u m b e r i s 729 . T h e n u m b e r c a n b e 123, 224, 325, 426, 527, 628, 729 .$

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A man engaged a worker on the condition that he would pay him Tk.30,000 and one uniform after one year of service. The worker served only 9 months and got Tk 22,000 and a uniform. What is the price of the uniform?