Problems on Numbersसंख्याओं पर आधारित प्रश्न questions and answersप्रश्न और उत्तर

How problems on numbers worksसंख्याओं पर आधारित प्रश्न को समझिए

A two-digit number with tens digit a and units digit b is 10a + b, not ab. Reversing its digits changes it by 9(b − a), so the change is always a multiple of 9 and dividing by 9 gives the difference of the digits directly. Together with the digit sum, that fixes the number.

When the sum and difference of two numbers are known, adding the two facts gives twice the larger number and subtracting gives twice the smaller. For consecutive numbers, centre the unknown on the middle one; the cross terms then cancel, as in (m − 2)² + m² + (m + 2)² = 3m² + 8.

Percentage questions about “a number” always use the original number as the base. If a number increased by 20% becomes 360, the number is 360 ÷ 1.2 = 300, not 360 − 20% of 360 = 288. Successive changes multiply: a 20% rise followed by a 10% fall is × 1.2 × 0.9 = × 1.08.

Each trick says when to use it, why it works and when it fails. Formula tricks are checked by code over their whole range.हर ट्रिक बताती है कि उसे कब इस्तेमाल करें, वह क्यों काम करती है और कब नहीं। सूत्र वाली ट्रिक्स को कोड से उनकी पूरी रेंज पर जाँचा गया है।

Answers and full solutions are shown. Hide them to test yourself first.उत्तर और पूरे हल दिखाए गए हैं। पहले खुद को परखने के लिए इन्हें छिपाइए।

1. Example 1उदाहरण 1 · Problems on numbers: digits, sums, differences and percentages · Easyआसान

   Ayaan and a friend from Lucknow have 261 cricket cards between them, and Ayaan has 109 more than the friend. How many cricket cards does Ayaan have?

   1. 76
   2. 152
   3. 185
   4. 370
   Answer:उत्तर: 185

   1. Larger = (261 + 109)/2 = 185.
   2. Smaller = (261 − 109)/2 = 76.
   3. Asked: the larger one, 185.

2. Example 2उदाहरण 2 · Problems on numbers: digits, sums, differences and percentages · Mediumमध्यम

   The number of visitors at a Kochi museum on a Sunday exceeds 2/7 of itself by 170. Find it.

   1. 68
   2. 121.4286
   3. 238
   4. 595
   Answer:उत्तर: 238

   1. N − (2/7)N = (5/7)N = 170.
   2. N = 170 × 7/5 = 238.

3. Example 3उदाहरण 3 · Problems on numbers: digits, sums, differences and percentages · Hardकठिन

   The sum of the squares of three consecutive natural numbers is 3,890. Harpreet wants to know the largest of them.

   1. 35
   2. 36
   3. 37
   4. 38
   Answer:उत्तर: 37

   1. (m − 1)² + m² + (m + 1)² = 3m² + 2 = 3,890.
   2. m² = 1,296, so m = 36.
   3. Numbers: 35, 36, 37; the largest is 37.

4. Example 4उदाहरण 4 · Problems on numbers: digits, sums, differences and percentages · Mediumमध्यम

   If a certain number is decreased by 15%, it becomes 697. What is the number?

   1. 592.45
   2. 712
   3. 801.55
   4. 820
   Answer:उत्तर: 820

   1. 85% of N = 697.
   2. N = 697 × 100 / 85 = 820.

5. Example 5उदाहरण 5 · Problems on numbers: digits, sums, differences and percentages · Mediumमध्यम

   A number exceeds 2/7 of itself by 155. Find the number.

   1. 62
   2. 110.7143
   3. 217
   4. 542.5
   Answer:उत्तर: 217

   1. N − (2/7)N = (5/7)N = 155.
   2. N = 155 × 7/5 = 217.

6. Example 6उदाहरण 6 · Problems on numbers: digits, sums, differences and percentages · Mediumमध्यम

   A number exceeds 5/9 of itself by 120. Find the number.

   1. 53.3333
   2. 150
   3. 216
   4. 270
   Answer:उत्तर: 270

   1. N − (5/9)N = (4/9)N = 120.
   2. N = 120 × 9/4 = 270.

Common mistakesआम गलतियाँ

• Answering with the reversed number instead of the original one.
• Undoing a percentage increase by subtracting the same percentage of the new value.
• Netting successive percentage changes as a simple difference (20% up, 10% down is +8%, not +10%).

Frequently asked questionsअक्सर पूछे जाने वाले प्रश्न