What is the value of 4 + 44 + 444 + 4444 + 44444 ?

Question

What is the value of 4 + 44 + 444 + 4444 + 44444 ?

1. A. 49380 (Correct answer)
2. B. 42300
3. C. 41300
4. D. 45000

Correct Answer

Option A — 49380

Detailed Solution & Explanation

The correct answer is 49380.

Key Points

• Add the terms directly: 4 + 44 = 48, + 444 = 492, + 4444 = 4,936, + 44,444 = 49,380.
• A faster route factors out the 4: the sum is 4 × (1 + 11 + 111 + 1,111 + 11,111) = 4 × 12,345 = 49,380.

Additional Information

• The repunit sum 1 + 11 + 111 + … has a memorable pattern: five terms give 12,345, four give 1,234, three give 123 — worth recognising on sight.
• The general form is a × (repunit sum), so 7 + 77 + 777 + 7,777 + 77,777 = 7 × 12,345 = 86,415.
• A units-digit check confirms the answer instantly: the five terms end in 4, 4, 4, 4, 4, summing to 20, so the total must end in 0 — which alone eliminates two options.

प्रश्न (हिन्दी में)

4 + 44 + 444 + 4444 + 44444 का मान क्या है?

1. A. 49380
2. B. 42300
3. C. 41300
4. D. 45000