Multiple choice

The ratio of two liquids in four jar is 1 : 2, 2 : 1, 3 : 1 and 2 : 3 respectively. If the ratio of their quantities in jar is 1 : 2 : 3 : 4. If all jar mixed up then what will be the ratio of two liquids in new mixture.

  1. $269 : 144$
  2. $445 : 331$
  3. $113 : 445$
  4. $331 : 269$

  5. None of these.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Jar ratios (liquid1:liquid2) are 1:2, 2:1, 3:1, 2:3 with quantities in ratio 1:2:3:4. Take quantities as x, 2x, 3x, 4x. Liquid1 total = 1×x + 2×2x + 3×3x + 2×4x = x+4x+9x+8x = 22x. Liquid2 total = 2×x + 1×2x + 1×3x + 3×4x = 2x+2x+3x+12x = 19x. Ratio = 22:19. This doesn't match any option. Let's use different approach: For jar1 with 3 parts (1:2), quantity x means x/3 and 2x/3. Jar2 (2:1) with 2x means 4x/3 and 2x/3. Jar3 (3:1) with 3x means 9x/4 and 3x/4. Jar4 (2:3) with 4x means 8x/5 and 12x/5. Summing: Liquid1 = x/3+4x/3+9x/4+8x/5, Liquid2 = 2x/3+2x/3+3x/4+12x/5. Computing LCM: Liquid1 = (20x+80x+135x+96x)/60 = 331x/60, Liquid2 = (40x+40x+45x+144x)/60 = 269x/60. Ratio = 331:269.

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