Directions Q. 36 to 40 are based on the following information.
The table below shows the percentage of students who passed an examination from different parts of the country in 1999.
Region
Percentage of Total Passed (1999)
Bihar
38%
UP
16%
Orissa
11%
WB
10%
Others
25%
The line graph below shows the percentage of freshers (students who passed their graduation in the same year) among the passed candidates from each region in 1999.
Question: 1
If in 1999 the total passed candidates from different parts of the country was 650, then how many non fresher candidates from Bihar passed the examination in 1999?
Show Hint
Find Bihar's total passed candidates using its pie share, then remove the freshers (from the line graph) to get non-freshers.
Step 1: Combine the two percentages first.
Instead of finding Bihar's total first, we can go straight to the non-fresher share of Bihar out of the whole 650, in one calculation.
Bihar contributes 38% of the total, and within Bihar, freshers are 20%, so non-freshers are $100\% - 20\% = 80\%$ of Bihar's candidates.
Step 2: Set up the combined fraction.
The Bihar non-freshers, as a fraction of the grand total of 650, work out to $38\% \times 80\%$.
\[ 0.38 \times 0.80 = 0.304 \]
So Bihar's non-freshers are 30.4% of the total 650 candidates.
Step 3: Apply this fraction to 650.
\[ 650 \times 0.304 = 197.6 \]
Rounding to the nearest whole candidate gives 198.
Step 4: Cross check against the sequential method.
Checking it the other way: Bihar total is $650 \times 0.38 = 247$; freshers are $247 \times 0.20 = 49.4$; non-freshers are $247 - 49.4 = 197.6$. Both routes agree.
Final Answer:
The non-fresher candidates from Bihar in 1999 come out to 198.
\[ \boxed{198} \]
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Question: 2
If in 1999 the total number of freshers from WB was 160, then how many non fresher candidates passed the exam from Others?
Show Hint
Use WB's freshers and its fresher rate to back out the grand total, then apply Others' share and non-fresher rate.
Step 1: Write WB's freshers as one combined fraction of the grand total.
WB freshers, as a share of the grand total $T$, equal WB's pie share (10%) times WB's fresher rate (25%) from the line graph.
\[ 160 = T \times 0.10 \times 0.25 = 0.025\,T \]
Step 2: Solve for the grand total in one step.
\[ T = \frac{160}{0.025} = 6400 \]
This skips the separate step of finding WB's own total first and reaches the grand total directly.
Step 3: Write Others' non-freshers as a combined fraction too.
Others' pie share is 25% and its fresher rate is 12%, so its non-fresher rate is $100\% - 12\% = 88\%$. Others' non-freshers, as a fraction of $T$, are $25\% \times 88\%$.
\[ 0.25 \times 0.88 = 0.22 \]
Step 4: Apply this fraction to the grand total.
\[ 6400 \times 0.22 = 1408 \]
Final Answer:
The number of non-fresher candidates who passed from Others in 1999 is 1408, matching the step-by-step build up.
\[ \boxed{1408} \]
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Question: 3
If total passed candidates from UP in 1999 was 112, what is the ratio between the number of freshers from Bihar and that of non fresher candidates from Orissa?
Show Hint
Both quantities are percentages of the same grand total, so the total cancels out of the ratio; simplify 0.38x0.20 against 0.11x0.85.
Step 1: Notice both quantities are a fixed fraction of the same grand total.
Let $T$ be the grand total. Bihar freshers are $T \times 0.38 \times 0.20 = 0.076T$. Orissa non-freshers are $T \times 0.11 \times 0.85 = 0.0935T$.
Step 2: Take the ratio and let the total cancel.
\[ \frac{\text{Bihar freshers}}{\text{Orissa non-freshers}} = \frac{0.076T}{0.0935T} = \frac{0.076}{0.0935} \]
The $T$ cancels out, so the UP figure of 112, which the sequential method needs to pin down $T$, is not even required here.
Step 3: Simplify the ratio of decimals.
Multiply top and bottom by 10000:
\[ \frac{0.076}{0.0935} = \frac{760}{935} \]
Both divide by 5:
\[ \frac{760}{935} = \frac{152}{187} \]
Step 4: Match against the options.
152:187 does not equal 760:187, 187:760 or 40:11. A quick check on option 3: $\frac{40}{11} = 3.64$, far from $\frac{152}{187} = 0.81$. None of the three stated ratios match.
Final Answer:
Since the worked-out ratio 152:187 is not one of the listed options, the correct choice is None of these.
\[ \boxed{\text{None of these}} \]
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Question: 4
If there is an increase of 10% and 20% candidates from Bihar and Others in the year 2000 respectively, and the number of total passed candidates from Orissa in 1999 was 77, what would be the approximate total passed candidates from Bihar and Others in 2000?
Show Hint
Use Orissa's 1999 figure to fix the grand total, grow Bihar by 10% and Others by 20%, then add and round.
Step 1: Get the grand total from Orissa's figure.
Orissa is 11% of the grand total $T$, and its 1999 count is 77, so $T = 77 / 0.11 = 700$.
Step 2: Write the combined 2000 total as one expression.
Instead of computing Bihar's and Others' 2000 counts separately and adding at the end, write the sum directly in terms of $T$.
\[ \text{2000 total (Bihar + Others)} = T(0.38 \times 1.10) + T(0.25 \times 1.20) = T(0.418 + 0.30) = 0.718T \]
Step 3: Substitute the grand total.
\[ 0.718 \times 700 = 502.6 \]
Step 4: Round to the closest option.
502.6 is nearest to 500 among the choices given (210, 480, 450, 500), so 500 is the approximate answer.
Final Answer:
Combining the growth of both regions into a single factor of 0.718 times the grand total gives the same approximate figure, 500.
\[ \boxed{500} \]
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Question: 5
If the non fresher candidates from UP in 1999 was 60, how many candidates passed the exam from all parts of the country?
Show Hint
Combine UP's pie share (16%) with its non-fresher rate (75%) to solve directly for the grand total from the 60 non-freshers.
Step 1: Write UP's non-freshers as one combined fraction of the grand total.
Let $T$ be the grand total. UP is 16% of $T$, and within UP, non-freshers are $100\% - 25\% = 75\%$. So UP's non-freshers, as a fraction of $T$, are $16\% \times 75\%$.
\[ 60 = T \times 0.16 \times 0.75 \]
Step 3: Solve for T in a single step.
\[ T = \frac{60}{0.12} = 500 \]
This reaches the grand total directly, without separately working out UP's own total of 80 candidates in between.
Step 4: Confirm against the choices.
500 matches option (1); the other options (300, 350, 450) would need a different combined percentage that does not fit the chart data.
Final Answer:
The total number of candidates who passed the exam from all parts of the country is 500.
\[ \boxed{500} \]
