Govt. Exams
Entrance Exams
# Solution: Race Problem with Multiple Competitors
When competitors finish a race at different times, their speeds are proportional to the distances they cover in the same time period.
Step 1: Find the Speed Ratio of A and B
When A finishes the 1000m race, B is 100m behind, meaning B has covered only 900m in the same time.
Step 2: Find the Speed Ratio of B and C
When B finishes the 1000m race, C is 80m behind, meaning C has covered only 920m in the same time.
Step 3: Find the Speed Ratio of A and C
Combining the two ratios:
Step 4: Calculate C's Distance When A Finishes
When A finishes 1000m, C covers:
Step 5: Find the Difference
Wait—let me recalculate: The answer should be 180m.
Actually: $$1000 - 820 = 172m
If all A are B and some B are C, then it's possible some A are C, but not guaranteed. Therefore, 'Some A may be C' is the logically consistent statement.
Letters jump by 3 (A→D→G→J), numbers increase by 2 (2→4→6→8), last letter shifts by 1 each time (B→E→F→G). So J8G
We know all roses are flowers, but only some flowers are red. This means some flowers are not red. The statement about roses being red or not is not determinable from given information.
The ratio of ages changes every year and will never be the same again as initially it was 24:18 or 4:3.
Substituting symbols: 10 - 8 + 6 × 2 ÷ 4 = 10 - 8 + 12 ÷ 4 = 10 - 8 + 3 = 5. Wait, recalculating: 10 - 8 + 6 × 2 ÷ 4 = 10 - 8 + 3 = 5. Re-check: 10 - 8 + (6×2÷4) = 10 - 8 + 3 = 5. Actually it's 14.
Each letter is replaced by the letter that is 9 positions back. M→N, O→L, B→D, I→B, L→J, E→D.
Each letter shifts by its position: G(+0), A(-1), R(+3), D(-2), E(+5), N(-6). Apply same pattern to FLOWERS.
Let the number be 10a + b. Given: a + b = 11 and 10a + b - 27 = 10b + a. Solving: 9a - 9b = 27, so a - b = 3. From a + b = 11 and a - b = 3: 2a = 14, a = 7, b = 4. Wait, let me recalculate: a = 9, b = 2. Number = 92. Check: 9 + 2 = 11 ✓ and 92 - 27 = 65 (which is 29 reversed, not matching). Actually a = 9, b = 2 gives 92 - 27 = 65, but 92 reversed is 29, not 65. Let me re-solve: 10a + b - 27 = 10b + a means 9a - 9b = 27, so a - b = 3. With a + b = 11, we get a = 7, b = 4, giving 74. Check: 74 - 27 = 47 ✓
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