Multiple choice

Directions: Read the information given below carefully and answer the question that follows. In a 70-litre mixture of diesel and kerosene, the ratio of diesel to kerosene is 9 : 5. ______ litres of kerosene and ______ litres of diesel must be added to make the ratio of diesel to kerosene as 11 : 10. Which of the following values can be put into the above blanks, respectively? (i) 25, 10 (ii) 25, 42 (iii) 35, 21 (iv) 35, 25 (v) 45, 32

  1. Only (i), (iii) and (v)

  2. Only (i), (iii) and (iv)

  3. Only (i), (ii) and (v)

  4. Only (ii), (iii) and (v)

  5. Only (ii), (iii) and (iv)
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A Correct answer
AI explanation

The initial 70-litre mixture contains (9/14 times 70) = 45 litres of diesel and (5/14 times 70) = 25 litres of kerosene. Testing the options by adding the given amounts of kerosene and diesel, we need the new ratio of diesel to kerosene to equal 11 to 10. For option (i) 25 and 10, the ratio is (45+10) to (25+25), which is 55 to 50, or 11 to 10. For option (iii) 35 and 21, the ratio is (45+21) to (25+35), which is 66 to 60, or 11 to 10. For option (v) 45 and 32, the ratio is (45+32) to (25+45), which is 77 to 70, or 11 to 10. Therefore, only options (i), (iii), and (v) work.

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