Question

What is the ratio of insured adults in Urban : Rural areas?

• A. \(82:65\)
• B. \(748:477\)
• C. \(65:82\)
• D. \(477:748\)
• A. \(18.75%\)
• B. \(20.17%\)
• C. \(22.50%\)
• D. \(25.00%\)
• A. \(1,494\)
• B. \(1,560\)
• C. \(1,620\)
• D. \(1,650\)
• A. \(22,800\)
• B. \(23,100\)
• C. \(24,300\)
• D. \(25,200\)
• A. \(48.50%\)
• B. \(49.75%\)
• C. \(50.86%\)
• D. \(52.00%\)
• A. \(52.15%\)
• B. \(56.25%\)
• C. \(61.25%\)
• D. \(64%\)

Answer 1

The Correct Option is B

Urban population = \(55%\) of \(1,80,000 = 99,000\). Insured in Urban = \((28+22+18)% = 68%\) of \(99,000 = 67,320\). Rural population = \(81,000\). Insured in Rural = \((35+10+8)% = 53%\) of \(81,000 = 42,930\). Thus the ratio: \[ \text{Urban : Rural} = 67,320 : 42,930 = 6,732 : 4,293 = 2,244:1,431 = 748:477. \]

Answer 2

Work with population-weighted percentages instead of raw counts. Urban insured share is \(68\%\) and Urban is \(55\%\) of the whole survey, so Urban insured is \(0.68 \times 0.55 = 0.374\) of the total. Rural insured share is \(53\%\) and Rural is \(45\%\) of the survey, giving \(0.53 \times 0.45 = 0.2385\) of the total. Comparing \(0.374 : 0.2385\) reduces to the same ratio as the raw counts, \(748:477\).

Answer 3

Since the exact insured counts work out to 67,320 in Urban and 42,930 in Rural, each candidate ratio can be tested by cross-multiplying against these two numbers rather than simplifying the ratio from scratch.

1. 82:65: Cross-multiplying, \(82 \times 42{,}930 = 3{,}520{,}260\) and \(65 \times 67{,}320 = 4{,}375{,}800\). These are not equal, so 82:65 is not the same ratio as 67,320:42,930.
2. 748:477: Cross-multiplying, \(748 \times 42{,}930 = 32{,}111{,}640\) and \(477 \times 67{,}320 = 32{,}111{,}640\). These match exactly, confirming this is the correct ratio.
3. 65:82: This is the previous wrong ratio flipped, so it fails the same cross-multiplication check, and it also has the wrong order since Urban's count is bigger than Rural's, not smaller.
4. 477:748: This is the correct ratio's two terms swapped. Since Urban insured (67,320) is larger than Rural insured (42,930), the first term of the ratio has to be the larger number, ruling out this reversed order.

Only 748:477 survives the cross-multiplication check against the actual insured counts.

So the correct answer is 748:477.

Answer 4

Uninsured in Urban = \(32%\) of \(99,000 = 31,680\). Uninsured in Rural = \(47%\) of \(81,000 = 38,070\). Difference: \[ 38,070 - 31,680 = 6,390. \] Percentage higher than Urban: \[ \frac{6,390}{31,680} \times 100 \approx 20.17%. \]

Answer 5

Express both uninsured groups as a share of the entire survey rather than computing counts first. Urban uninsured is \(32\%\) of \(55\%\), or \(17.6\%\) of everyone, and Rural uninsured is \(47\%\) of \(45\%\), or \(21.15\%\) of everyone. The gap between these, \(21.15 - 17.6 = 3.55\) percentage points of the whole survey, corresponds to about \(6,390\) people. Measuring this gap against the Urban uninsured count of \(31,680\) gives the same \(20.17\%\) figure.

Answer 6

Each option states a percentage increase from Urban's uninsured count to Rural's; that claim can be tested directly by applying it to Urban's count of 31,680 and checking whether it lands on Rural's count of 38,070.

1. 18.75%: Increasing 31,680 by 18.75% gives \(31{,}680 \times 1.1875 \approx 37{,}620\), which falls short of 38,070, so this percentage is too small.
2. 20.17%: Increasing 31,680 by 20.17% gives \(31{,}680 \times 1.2017 \approx 38{,}070\), matching Rural's uninsured count exactly.
3. 22.50%: Increasing 31,680 by 22.50% gives \(31{,}680 \times 1.225 \approx 38{,}808\), overshooting 38,070, so this percentage is too large.
4. 25.00%: Increasing 31,680 by 25% gives \(31{,}680 \times 1.25 = 39{,}600\), well past 38,070, making this option even further off.

Only a 20.17% increase applied to Urban's uninsured count reproduces Rural's actual uninsured count.

So the correct answer is 20.17%.

Answer 7

This year: Private (Urban) \(=\;22%\) of \(99,000 = 21,780\). Private (Rural) \(=\;10%\) of \(81,000 = 8,100\). Total Private now \(= 29,880\). Next year: Total population grows by \(5%\): \(1,80,000 \to 1,89,000\). Urban \(=55%\) of \(1,89,000 = 1,03,950\). Rural \(= 85,050\). Private (Urban) next year \(=22%\) of \(1,03,950 = 22,869\). Private (Rural) next year \(=10%\) of \(85,050 = 8,505\). Total Private next year \(= 31,374\). Increase: \[ 31,374 - 29,880 = 1,494. \]

Answer 8

Because every share, including the Urban-Rural split, stays exactly fixed, the total privately insured figure simply scales with the population by the same \(5\%\) factor, with no need to track Urban and Rural separately. This year's total private-insured count is \(21,780 + 8,100 = 29,880\). Scaling this by \(5\%\) directly gives the increase: \(29,880 \times 0.05 = 1,494\).

Answer 9

Since every percentage share stays fixed and only the total population grows by 5%, the entire increase in privately insured people has to equal exactly 5% of however many are privately insured this year. That figure can be checked against each option.

1. 1,494: This year's total private insured is \(21{,}780 + 8{,}100 = 29{,}880\). Five percent of that is \(29{,}880 \times 0.05 = 1{,}494\), matching this option exactly.
2. 1,560: Dividing this by 29,880 gives about 5.22%, not the 5% growth rate stated in the question, so this option assumes a slightly wrong growth rate.
3. 1,620: This works out to about 5.42% of 29,880, again inconsistent with the fixed 5% population growth rate.
4. 1,650: This is about 5.52% of 29,880, the furthest of the four from matching a genuine 5% increase.

Because the shares don't change, the private-insured increase has to be exactly 5% of this year's private-insured total, and only 1,494 satisfies that.

So the correct answer is 1,494.

Answer 10

Employer coverage (Urban) \(=\;18%\) of \(99,000 = 17,820\). Employer coverage (Rural) \(=\;8%\) of \(81,000 = 6,480\). Total Employer-covered: \[ 17,820 + 6,480 = 24,300. \]

Answer 11

A quick estimate narrows this down fast: Urban employer coverage is roughly \(18\%\) of about \(99,000\) (\(\approx 17,800\)), and Rural is roughly \(8\%\) of about \(81,000\) (\(\approx 6,500\)). Adding these gives close to \(24,300\), which already rules out \(22,800\) and \(23,100\) as too low and \(25,200\) as too high. Working the exact figures, \(18\%\) of \(99,000 = 17,820\) and \(8\%\) of \(81,000 = 6,480\), confirms the total as \(17,820 + 6,480 = 24,300\).

Answer 12

Since the combined Employer rate across the whole survey works out to a single blended percentage, each option can be checked against that percentage of the full 1,80,000 population.

1. 22,800: This is about 12.67% of 1,80,000, lower than the blended Employer rate the survey's numbers actually produce.
2. 23,100: This comes to about 12.83% of 1,80,000, still short of the true blended rate.
3. 24,300: This is exactly 13.5% of 1,80,000, and 13.5% is precisely the population-weighted Employer rate: \(18\% \times 55\% + 8\% \times 45\% = 9.9\% + 3.6\% = 13.5\%\).
4. 25,200: This is 14% of 1,80,000, overshooting the true blended rate of 13.5%.

The blended Employer rate across both areas comes to 13.5% of the full survey, and 13.5% of 1,80,000 is 24,300.

So the correct answer is 24,300.

Answer 13

Public (Urban) \(=\;28%\) of \(99,000 = 27,720\). Public (Rural) \(=\;35%\) of \(81,000 = 28,350\). Total Public insured: \[ 27,720 + 28,350 = 56,070. \] Total insured adults: \[ \text{Urban insured} = 68% \text{ of } 99,000 = 67,320, \] \[ \text{Rural insured} = 53% \text{ of } 81,000 = 42,930, \] \[ \Rightarrow \text{Total insured} = 1,10,250. \] Percentage of insured who are Public: \[ \frac{56,070}{1,10,250} \times 100 \approx 50.86%. \]

Answer 14

Stay in percentage-of-population terms throughout instead of computing raw counts twice. Public coverage contributes \(28\% \times 55\% + 35\% \times 45\% = 15.4\% + 15.75\% = 31.15\%\) of the whole population, while total insured contributes \(68\% \times 55\% + 53\% \times 45\% = 37.4\% + 23.85\% = 61.25\%\) of the whole population. The Public share of insured people is then \(31.15 / 61.25 \times 100 \approx 50.86\%\), the same result reached through raw head counts.

Answer 15

With Public insured at 56,070 and total insured at 1,10,250 already established, each percentage option can be tested by multiplying it back against 1,10,250 to see which one returns 56,070.

1. 48.50%: \(48.50\%\) of \(1{,}10{,}250 \approx 53{,}471\), short of the actual 56,070 Public figure.
2. 49.75%: \(49.75\%\) of \(1{,}10{,}250 \approx 54{,}850\), still below 56,070.
3. 50.86%: \(50.86\%\) of \(1{,}10{,}250 \approx 56{,}072\), matching the actual Public insured count of 56,070, the small gap being rounding.
4. 52.00%: \(52\%\) of \(1{,}10{,}250 = 57{,}330\), overshooting the actual figure.

Only 50.86% reproduces the true Public insured count of 56,070 when applied back to the total insured figure.

So the correct answer is 50.86%.

Answer 16

Total insured adults (from above) = \(1,10,250\). Total surveyed population = \(1,80,000\). Thus: \[ \frac{1,10,250}{1,80,000} \times 100 = \frac{11,025}{18,000} \times 100 = 0.6125 \times 100 = 61.25%. \]

Answer 17

Blend the two insured percentages by their population weights directly rather than converting to head counts. Urban contributes \(68\%\) at a \(0.55\) weight, and Rural contributes \(53\%\) at a \(0.45\) weight: \(68 \times 0.55 + 53 \times 0.45 = 37.4 + 23.85 = 61.25\). This weighted average is exactly the overall percentage of the survey that is insured.

Answer 18

With the total insured count already known to be 1,10,250 out of 1,80,000 surveyed, each percentage option can be tested by multiplying it back against 1,80,000.

1. 52.15%: \(52.15\%\) of \(1{,}80{,}000 = 93{,}870\), far short of the actual 1,10,250 insured count.
2. 56.25%: \(56.25\%\) of \(1{,}80{,}000 = 1{,}01{,}250\), still below the true count.
3. 61.25%: \(61.25\%\) of \(1{,}80{,}000 = 1{,}10{,}250\), matching the actual insured count exactly.
4. 64%: \(64\%\) of \(1{,}80{,}000 = 1{,}15{,}200\), overshooting the true count.

Only 61.25% reproduces the actual insured count of 1,10,250 when applied to the full surveyed population.

So the correct answer is 61.25%.