IPMAT Indore 2020 — LRDI

The Setup: Every question in this set runs on one rule, so it is worth nailing down once here. The table gives two prices per day, and the passage defines them from the *investor's* side: you buy at the Buy price and sell at the Sell price. The Buy price is always the higher of the two, so the market takes a small bite on every round trip. Mixing the two columns up is the single biggest source of wrong answers in this caselet.
Step 1: Fix the method. With a fixed pot of money you cannot own a fraction of a share, so:

$$\text{Shares}=\left\lfloor\frac{\text{Capital}}{\text{Monday Buy price}}\right\rfloor, \qquad \text{Residual cash}=\text{Capital}-\text{Shares}\times\text{Buy price}$$

$$\text{Final wealth}=\text{Shares}\times\text{Friday Sell price}+\text{Residual cash}$$

The residual is the small change that could not buy one more share. It does not vanish - it stays in the investor's pocket and counts toward the final wealth. It barely matters here, but in MCQ 17 it decides the answer outright, so build the habit now.
Step 2: Run all four candidates. Capital is Rs 36,00,000. Buy at Monday's Buy price, sell at Friday's Sell price.

Two share counts are worth checking by hand, because rounding the wrong way is easy here:

$$3046\times 1181=35,97,326\leq 36,00,000 \quad\text{but}\quad 3046\times 1182=36,00,372>36,00,000$$

so Britannia buys 1,181 shares, not 1,182. Likewise $346\times 10404=35,99,784$ fits while $346\times 10405=36,00,130$ does not.
Step 3: Read off the winner. Marico returns the largest profit at roughly Rs 2.70 lakh, comfortably ahead of ITC's Rs 2.27 lakh.
Step 4: Sanity-check why. Marico wins on percentage movement, not on price. It rose from 346 to 372, a gain of about $7.5\%$, versus ITC's $6.3\%$, Britannia's $3.1\%$ and HUL's $1.7\%$. Because the whole pot goes into one stock either way, the cheapest share price is irrelevant - only the percentage gain matters, and a quick ratio scan of $\frac{\text{Fri Sell}}{\text{Mon Buy}}$ would have identified Marico without computing a single share count.

Final Answer: Marico

The Setup: A two-leg trade: HUL from Monday to Wednesday, then the entire proceeds into Britannia from Wednesday to Friday. Using the convention from MCQ 16 - buy at the Buy price, sell at the Sell price, and carry the residual cash forward. That last point is not bookkeeping pedantry here; it is what separates two of the four options.
Step 1: Leg one - HUL, Monday to Wednesday. Monday Buy price is 1,933:

$$\text{Shares}=\left\lfloor\frac{36,00,000}{1933}\right\rfloor=1862, \qquad \text{Residual}=36,00,000-1862\times 1933=754$$

Sell on Wednesday at HUL's Sell price of 1,979:

$$1862\times 1979=36,84,898 \implies \text{Total cash}=36,84,898+754=36,85,652$$

Step 2: Leg two - Britannia, Wednesday to Friday. Wednesday Buy price is 3,115:

$$\left\lfloor\frac{36,85,652}{3115}\right\rfloor=1183 \quad\text{since}\quad 3115\times 1183=36,85,045\leq 36,85,652$$

This is the hinge of the whole question. Had we thrown away the Rs 754 left over from the HUL leg, the available cash would be 36,84,898 - and $36,85,045>36,84,898$, so only 1,182 shares would be affordable. That stray Rs 754 is precisely what pays for the 1,183rd share, and that one share is worth about Rs 3,140 by Friday. Discarding it drops the answer to $3.10\%$ and lands you on the wrong option.
Step 3: Close the position. Sell on Friday at Britannia's Sell price of 3,140, and add the residual from this leg ($36,85,652-36,85,045=607$):

$$1183\times 3140=37,14,620 \implies \text{Final wealth}=37,14,620+607=37,15,227$$

Step 4: Compute the return.

$$\text{Return}=\frac{37,15,227-36,00,000}{36,00,000}\times 100=\frac{1,15,227}{36,00,000}\times 100=3.2008\%\approx 3.20\%$$

Step 5: Confirm with a shortcut. Ignore the share-counting entirely and just compound the two price ratios, which is what the trade does at heart:

$$\frac{1979}{1933}\times\frac{3140}{3115}=1.03201 \implies 3.20\%$$

Both routes agree to two decimal places, which confirms the answer is robust and not an artefact of rounding.

Final Answer: 3.20 percent

The Setup: The spread is defined in the stem as the gap between the quoted buy and sell price of a stock - the market's cut on a round trip. So for each day we take $\text{Buy}-\text{Sell}$ for all five stocks and average the five numbers. Since every day has the same five stocks, comparing the totals is enough and the division by 5 is only cosmetic.
Step 1: Compute the spread for each stock, day by day.

Worked out in full for Monday, the winning day:

$$\frac{(462-460)+(346-345)+(1933-1931)+(238-237)+(3046-3044)}{5}=\frac{2+1+2+1+2}{5}=\frac{8}{5}=1.6$$

Step 2: Compare. Monday's average of 1.6 is the lowest of the four days offered; Tuesday at 1.8 is the nearest rival.
Step 3: Note the shortcut. Monday's total of 8 is the smallest total in the table, and no division was needed to see it. Monday is also the only day where three of the five stocks trade at a spread of just 1 or 2 across the board - it is the tightest, most liquid-looking day of the week.

Final Answer: Monday

The Setup: The commission is charged on the value of shares bought or sold, so it applies twice - once on the purchase leg and once on the sale leg - and each leg is valued at its own price. Using the convention from MCQ 16: the investor buys at Tuesday's Buy price and sells at Thursday's Sell price.
Step 1: The buying leg, Tuesday. Britannia's Tuesday Buy price is 3,101:

$$\text{Value}=1000\times 3101=31,01,000 \implies \text{Fee}=31,01,000\times 0.1\%=3101$$

Step 2: The selling leg, Thursday. Britannia's Thursday Sell price is 3,025:

$$\text{Value}=1000\times 3025=30,25,000 \implies \text{Fee}=30,25,000\times 0.1\%=3025$$

Note that $0.1\%$ of a value is just that value divided by 1,000 - and since exactly 1,000 shares were traded, each fee comes out equal to the share price itself. That is a pleasant shortcut, not a coincidence to rely on generally.
Step 3: Total the two legs.

$$3101+3025=6126$$

Step 4: Read the option list - it is a trap laid with real precision. All four options are within Rs 3 of each other, because each one corresponds to a different mix-up of the Buy and Sell columns:

There is no arithmetic in this question at all once you know which column to read; the entire difficulty is the convention. You buy at Buy and sell at Sell.

Final Answer: 6,126

The Setup: The purchase is fixed - ITC bought on Monday - and only the exit day is ours to choose. Using the convention from MCQ 16: buy at Monday's Buy price of 238, sell at the chosen day's Sell price.
Step 1: Note why no calculation is really needed. Monday's purchase locks in a fixed share count:

$$\left\lfloor\frac{36,00,000}{238}\right\rfloor=15,126 \text{ shares, with Rs 12 left over}$$

That count does not change with the exit day, and the residual is fixed too. So the final wealth is $15,126\times(\text{Sell price})+12$, which is strictly increasing in the sell price. Maximising profit is therefore identical to maximising ITC's Sell price, and the whole question collapses into scanning one row of the table.
Step 2: Scan ITC's Sell prices.

Step 3: Read off the answer. Friday's Sell price of 253 is the highest of the week, giving the maximum profit of about Rs 2.27 lakh. Thursday is the trap for anyone glancing at the Buy column or misreading the row - ITC dips to 221 that day, which would actually book a loss of roughly Rs 2.57 lakh against a purchase price of 238.
Step 4: Sanity check. Selling on Tuesday at 238 exactly matches Monday's Buy price of 238, so that trade nets zero profit - a useful confirmation that the buy and sell columns are being read the right way round.

Final Answer: Friday