• Math

  Ratio and Proportion (Class 7)

  Posted by Eshita Basak on June 23, 2023 at 8:46 pm

  Two numbers are in ratio 7:12. On adding 7 to the first and 2 to the second number, the ratio becomes 21:31. Find both the numbers.

  Shankhadeep Bose replied 1 year, 2 months ago 2 Members · 1 Reply
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  Shankhadeep Bose

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  June 23, 2023 at 9:23 pm

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  Let’s assume the two numbers in the ratio 7:12 are 7x and 12x, where x is a common multiplier.

  According to the given condition, when 7 is added to the first number and 2 is added to the second number, the new ratio becomes 21:31.

  So, after adding 7 to the first number, it becomes 7x + 7, and after adding 2 to the second number, it becomes 12x + 2.

  Now, we can set up the equation based on the new ratio:

  (7x + 7) / (12x + 2) = 21/31

  To eliminate the fractions, after cross-multiplying:

  (7x + 7) * 31 = (12x + 2) * 21

  217x + 217 = 252x + 42

  Subtracting 217x from both sides, we get:

  217 = 35x + 42

  Subtracting 42 from both sides, we get:

  175 = 35x

  Dividing both sides by 35, we get:

  x = 5

  Now, we can find the values of the two numbers:

  First number = 7x = 7 * 5 = 35; Second number = 12x = 12 * 5 = 60

  Answer: The two numbers are 35 and 60.

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