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ABHYAS PREP: ADVANCED QUANT · PROBLEMS ON NUMBERS

Problems on numbers: digits, sums, differences and percentages

Write a two-digit number as 10a + b; reversing it changes the value by 9 × (difference of digits). For percentages, the base is the number before the change.

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Worked examples

Example 1 · level 1

Aditya thinks of a two-digit number. The sum of its digits is 8. When the digits are reversed, the number decreases by 54. What is the number?

  1. 17
  2. 62
  3. 71
  4. 82
Show solution
  1. a + b = 8.
  2. (10b + a) − (10a + b) = 9(b − a) = −54 ⇒ a − b = 6.
  3. So a = 7, b = 1; the number is 71.

Answer: 71

Example 2 · level 2

The number of visitors at a Surat museum on a Sunday exceeds 1/4 of itself by 54. Find it.

  1. 18
  2. 40.5
  3. 72
  4. 216
Show solution
  1. N − (1/4)N = (3/4)N = 54.
  2. N = 54 × 4/3 = 72.

Answer: 72

Example 3 · level 3

The population of a village was first increased by 25% and then decreased by 40%. The result is 1,950. What was the starting figure?

  1. 1,462.5
  2. 2,047.5
  3. 2,294.1176
  4. 2,600
Show solution
  1. N × 1.25 × 0.6 = 1,950.
  2. N = 1,950 ÷ 0.75 = 2,600.

Answer: 2,600

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