Directions: The following table shows the number of candidates trained by five institutes and the training fee charged per candidate during a particular session. Study the table carefully and answer the questions that follow.

Institute	Candidates Trained	Fee per Candidate (₹)
A	240	18,000
B	300	16,000
C	180	24,000
D	360	15,000
E	220	20,000

Institute D originally trains 360 candidates at ₹ 15,000 each. Both figures change, so recompute each one before multiplying.

Candidates fall by 20%: \(360 \times 0.80 = 288\).

Fee rises by 25%: \(15{,}000 \times 1.25 = 18{,}750\).

The new collection is \(288 \times 18{,}750 = 54{,}00{,}000\).

The result is worth a second look: a 20% fall paired with a 25% rise means the collection is multiplied by \(0.80 \times 1.25 = 1\), so the fee collected is exactly what it was before the changes.

Hence, the fee collected by Institute D is ₹ 54,00,000.

Institute B's fee rises by 25%, so its new fee per candidate is \(16{,}000 \times 1.25 = 20{,}000\), while its 300 candidates stay unchanged. Every other institute is untouched.

Now multiply candidates by fee for each institute:

A: \(240 \times 18{,}000 = 43{,}20{,}000\); B: \(300 \times 20{,}000 = 60{,}00{,}000\); C: \(180 \times 24{,}000 = 43{,}20{,}000\).

D: \(360 \times 15{,}000 = 54{,}00{,}000\); E: \(220 \times 20{,}000 = 44{,}00{,}000\).

Adding the five figures gives \(43{,}20{,}000 + 60{,}00{,}000 + 43{,}20{,}000 + 54{,}00{,}000 + 44{,}00{,}000 = 2{,}44{,}40{,}000\).

Hence, the new total fee collected is ₹ 2,44,40,000.

Split the institutes by size first. Those training 250 or fewer are A (240), C (180) and E (220); those training more than 250 are B (300) and D (360).

For the first group the total fee is \(43{,}20{,}000 + 43{,}20{,}000 + 44{,}00{,}000 = 1{,}30{,}40{,}000\) over \(240 + 180 + 220 = 640\) candidates, so the weighted average is \(\frac{1{,}30{,}40{,}000}{640} = 20{,}375\).

For the second group the total fee is \(48{,}00{,}000 + 54{,}00{,}000 = 1{,}02{,}00{,}000\) over \(300 + 360 = 660\) candidates, so the weighted average is \(\frac{1{,}02{,}00{,}000}{660} = \frac{1{,}70{,}000}{11} \approx 15{,}454.55\).

The excess is \(20{,}375 - \frac{1{,}70{,}000}{11} = \frac{2{,}24{,}125 - 1{,}70{,}000}{11} = \frac{54{,}125}{11} \approx 4{,}920.45\).

Hence, the weighted average fee exceeds the other by ₹ 4,920·45.

The total collection is the sum of candidates multiplied by fee for each of the five institutes.

A: \(240 \times 18{,}000 = 43{,}20{,}000\); B: \(300 \times 16{,}000 = 48{,}00{,}000\); C: \(180 \times 24{,}000 = 43{,}20{,}000\).

D: \(360 \times 15{,}000 = 54{,}00{,}000\); E: \(220 \times 20{,}000 = 44{,}00{,}000\).

Adding them gives \(43{,}20{,}000 + 48{,}00{,}000 + 43{,}20{,}000 + 54{,}00{,}000 + 44{,}00{,}000 = 2{,}32{,}40{,}000\).

Hence, the total fee collected by all five institutes is ₹ 2,32,40,000.

Compute each institute's collection as candidates multiplied by fee, then group them as the question asks.

Institutes A and C together collect \(240 \times 18{,}000 + 180 \times 24{,}000 = 43{,}20{,}000 + 43{,}20{,}000 = 86{,}40{,}000\).

Institutes D and E together collect \(360 \times 15{,}000 + 220 \times 20{,}000 = 54{,}00{,}000 + 44{,}00{,}000 = 98{,}00{,}000\).

The ratio is \(86{,}40{,}000 : 98{,}00{,}000 = 864 : 980\), and dividing both terms by 4 gives \(216 : 245\), which has no further common factor.

Hence, the ratio is 216 : 245.