Problem solving ( show your calculation step)

A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if these two digits are reversed. What is the number?

Created: 4 weeks ago | Updated: 3 weeks ago

Job Solution Dutch-Bangla Bank Ltd Dutch- Bangla Bank Ltd. Recruitment Test for Assistance Officer Examination Held on : 18.03.2017 || 2017 গণিত

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প্রশ্নে বলা হচ্ছে, তিন সংখ্যা বিশিষ্ট একটি সংখ্যার তিনটির যোগফল 10. মাঝের অঙ্কটি অন্য দুটি সংখ্যার সমষ্টির সমান এবং ঐ দুটি সংখ্যা স্থান বিনিময় করলে যে সংখ্যাটি পাওয়া যায় তা মূল সংখ্যার চেয়ে 99 বেশি হলে সংখ্যাটি কত?

$L e t, t h e H u n d r e d t h d i g i t i s x, T e n t h d i g i t s i s y A n d U n i t d i g i t s i s z ∴ T h e n u m b e r i s (100 x + 10 y + z) A c c o r d i n g t o q u e s t i o n, x + y + z = 10 . . . . . . . . . . . . . . . . (i) y = x + z . . . . . . . . . . . . . . . (i i) 100 x + 10 y + z + 99 = 100 z + 10 y + x . . . . . . . . . . . . . . . . (i i i)$

From equation (iii)

$100 x + 10 y + z + 99 = 100 z + 10 y + x \Rightarrow 100 x + z + 99 + 10 y - 10 y = 100 z + x \Rightarrow 100 x + z + 99 = 100 z + x \Rightarrow 100 z - z + x - 100 z = 99 \Rightarrow 99 z - 99 x = 99 \Rightarrow 99 (z - x) = 99 \Rightarrow (z - x) = \frac{99}{99} \Rightarrow z - x = 1 ∴ z = x + 1 . . . . . . . . . . . . . . . . . . . . . . . . (i v)$

putting the value of z in equation (ii)

$y = z + x \Rightarrow y = x + x + 1 \Rightarrow y = 2 x + 1 . . . . . . . . . . . . . . . . (v)$

putting the value of y & z in equation (i)

$x + y + z = 20 \Rightarrow x + 2 x + 1 + x + 1 = 10 \Rightarrow 4 x + 2 = 10 \Rightarrow 4 x = 10 - 2 \Rightarrow 4 x = 8 \Rightarrow x = \frac{8}{4} ∴ x = 2$

putting the value of x in equation (v)

$y = 2 x + 1 \Rightarrow y = 2 \times 2 + 1 \Rightarrow y = 4 + 1 ∴ y = 5$

putting the value of x in equation (iv)

$z = x + 1 \Rightarrow z = 2 + 1 ∴ z = 3$

The number will be $= 100 x + 10 y + z = (100 \times 2) + (10 \times 5) + (3 \times 1) = 200 + 50 + 3 = 253$

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Problem solving ( show your calculation step)

A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if these two digits are reversed. What is the number?

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