Apedia Logo Apedia
Join

Choose Language

Select your preferred reading language
🇬🇧
English
✔
🇮🇳
हिन्दी
✔
✕
Full View
Algebra
Linear Equations
EN हिंदी
✕
NTPC Graduate Tier 1 2016 Shift 2 📅 02 Apr, 2016

The sum of digits of a two-digit number is 9. When the digits are reversed, the number decreases by 45. Find the changed number.

A
45
B
72
C
63
D
27
Result Summary
Logo

APEDIA

NTPC Graduate Tier 1
2016 • 02 Apr, 2016 • Shift 2
The sum of digits of a two-digit number is 9. When the digits are reversed, the number decreases by 45. Find the changed number.
Correct Answer
27
Variable Setup: Let the unknown two-digit number be algebraically represented as 10x + y, where x and y represent the specific digits. The first condition dicta......
Ref/Book : NTPC Graduate Tier 1 2016
Ref. Subject Algebra
Chapter -
Ref. Topic Linear Equations
Pg. No -
💡 Analysis & Explanation
Variable Setup ▼
Let the unknown two-digit number be algebraically represented as 10x + y, where x and y represent the specific digits. The first condition dictates x + y = 9.
Reversal Equation ▼
Reversing the positional digits natively creates the new number 10y + x. The given condition explicitly states that the original number strictly decreases by 45 upon reversal, generating the equation (10x + y) - (10y + x) = 45. This systematically simplifies to 9x - 9y = 45, or x - y = 5.
Solving the System ▼
We successfully possess two linear equations: x + y = 9 and x - y = 5. Adding them systematically yields 2x = 14, isolating x as 7. Substituting x back into the equation reveals y = 2. The original starting number is 72.
Final Target Context ▼
The prompt specifically and carefully asks for the 'changed' (reversed) number, which corresponds to 27.
Conclusion ▼
The required reversed numerical output is strictly 27.
← Prev
93 / 100
Next →