The opening prices on Monday of four stocks A, B, C and D were ₹200, ₹400, ₹250 and ₹500 respectively. The table below shows the percentage change in each stock's price on each day of the week (Monday to Friday). For Monday, the change is measured from Monday's opening price to Monday's closing price; for every later day, the change is measured from the previous day's closing price to that day's closing price.
| Stock | Mon | Tue | Wed | Thu | Fri |
|---|---|---|---|---|---|
| A | +10% | −5% | +20% | −25% | +10% |
| B | −5% | +10% | −10% | +5% | +20% |
| C | +20% | +20% | −25% | −10% | +10% |
| D | −10% | +5% | +10% | −20% | +25% |
Assume shares can be bought or sold only at the closing price of a day, except where the Monday opening price is explicitly mentioned. Ignore brokerage and taxes.
| Stock | Mon | Tue | Wed | Thu | Fri |
|---|---|---|---|---|---|
| A | +10% | −5% | +20% | −25% | +10% |
| B | −5% | +10% | −10% | +5% | +20% |
| C | +20% | +20% | −25% | −10% | +10% |
| D | −10% | +5% | +10% | −20% | +25% |
Assume shares can be bought or sold only at the closing price of a day, except where the Monday opening price is explicitly mentioned. Ignore brokerage and taxes.
Question 1
Single correct option
Which stock showed the highest percentage increase from its Monday opening price to its Friday closing price?
- A. A
- B. B
- C. C
- D. D
Show answer and solution
Answer: (B) B
Closing prices (₹), computed by applying the successive changes:
| Stock | Mon | Tue | Wed | Thu | Fri |
|---|---|---|---|---|---|
| A | 220 | 209 | 250.8 | 188.1 | 206.91 |
| B | 380 | 418 | 376.2 | 395.01 | 474.01 |
| C | 300 | 360 | 270 | 243 | 267.3 |
| D | 450 | 472.5 | 519.75 | 415.8 | 519.75 |
| Total | 1350 | 1459.5 | 1416.75 | 1241.91 | 1467.97 |
Weekly change = product of daily factors − 1:
A: 1.1 × 0.95 × 1.2 × 0.75 × 1.1 ≈ 1.0346 → +3.5%
B: 0.95 × 1.1 × 0.9 × 1.05 × 1.2 ≈ 1.1850 → +18.5%
C: 1.2 × 1.2 × 0.75 × 0.9 × 1.1 ≈ 1.0692 → +6.9%
D: 0.9 × 1.05 × 1.1 × 0.8 × 1.25 ≈ 1.0395 → +3.95%
Highest: B. Note that A and D have the same simple sum of percentages (+10%) but different compounded results — always multiply the factors.
| Stock | Mon | Tue | Wed | Thu | Fri |
|---|---|---|---|---|---|
| A | 220 | 209 | 250.8 | 188.1 | 206.91 |
| B | 380 | 418 | 376.2 | 395.01 | 474.01 |
| C | 300 | 360 | 270 | 243 | 267.3 |
| D | 450 | 472.5 | 519.75 | 415.8 | 519.75 |
| Total | 1350 | 1459.5 | 1416.75 | 1241.91 | 1467.97 |
Weekly change = product of daily factors − 1:
A: 1.1 × 0.95 × 1.2 × 0.75 × 1.1 ≈ 1.0346 → +3.5%
B: 0.95 × 1.1 × 0.9 × 1.05 × 1.2 ≈ 1.1850 → +18.5%
C: 1.2 × 1.2 × 0.75 × 0.9 × 1.1 ≈ 1.0692 → +6.9%
D: 0.9 × 1.05 × 1.1 × 0.8 × 1.25 ≈ 1.0395 → +3.95%
Highest: B. Note that A and D have the same simple sum of percentages (+10%) but different compounded results — always multiply the factors.
Question 2
Single correct option
For how many of the four stocks was the Friday closing price higher than the Monday closing price?
- A. 1
- B. 2
- C. 3
- D. 4
Show answer and solution
Answer: (B) 2
Closing prices (₹), computed by applying the successive changes:
| Stock | Mon | Tue | Wed | Thu | Fri |
|---|---|---|---|---|---|
| A | 220 | 209 | 250.8 | 188.1 | 206.91 |
| B | 380 | 418 | 376.2 | 395.01 | 474.01 |
| C | 300 | 360 | 270 | 243 | 267.3 |
| D | 450 | 472.5 | 519.75 | 415.8 | 519.75 |
| Total | 1350 | 1459.5 | 1416.75 | 1241.91 | 1467.97 |
Compare Friday vs Monday close: A 206.91 < 220 ✗; B 474.01 > 380 ✓; C 267.3 < 300 ✗; D 519.75 > 450 ✓.
Answer: 2 stocks (B and D).
Shortcut: Multiply only the Tue–Fri factors: A 0.95×1.2×0.75×1.1 = 0.9405 < 1; C 1.2×0.75×0.9×1.1 = 0.891 < 1; B and D exceed 1.
| Stock | Mon | Tue | Wed | Thu | Fri |
|---|---|---|---|---|---|
| A | 220 | 209 | 250.8 | 188.1 | 206.91 |
| B | 380 | 418 | 376.2 | 395.01 | 474.01 |
| C | 300 | 360 | 270 | 243 | 267.3 |
| D | 450 | 472.5 | 519.75 | 415.8 | 519.75 |
| Total | 1350 | 1459.5 | 1416.75 | 1241.91 | 1467.97 |
Compare Friday vs Monday close: A 206.91 < 220 ✗; B 474.01 > 380 ✓; C 267.3 < 300 ✗; D 519.75 > 450 ✓.
Answer: 2 stocks (B and D).
Shortcut: Multiply only the Tue–Fri factors: A 0.95×1.2×0.75×1.1 = 0.9405 < 1; C 1.2×0.75×0.9×1.1 = 0.891 < 1; B and D exceed 1.
Question 3
Single correct option
An investor held one share of each of the four stocks throughout the week. On which day was the total closing value of her holding the lowest?
- A. Monday
- B. Tuesday
- C. Wednesday
- D. Thursday
Show answer and solution
Answer: (D) Thursday
Closing prices (₹), computed by applying the successive changes:
| Stock | Mon | Tue | Wed | Thu | Fri |
|---|---|---|---|---|---|
| A | 220 | 209 | 250.8 | 188.1 | 206.91 |
| B | 380 | 418 | 376.2 | 395.01 | 474.01 |
| C | 300 | 360 | 270 | 243 | 267.3 |
| D | 450 | 472.5 | 519.75 | 415.8 | 519.75 |
| Total | 1350 | 1459.5 | 1416.75 | 1241.91 | 1467.97 |
Total closing values: Mon 1350, Tue 1459.5, Wed 1416.75, Thu 1241.91, Fri 1467.97. The lowest is on Thursday, when A, C and D all fell sharply (−25%, −10%, −20%).
| Stock | Mon | Tue | Wed | Thu | Fri |
|---|---|---|---|---|---|
| A | 220 | 209 | 250.8 | 188.1 | 206.91 |
| B | 380 | 418 | 376.2 | 395.01 | 474.01 |
| C | 300 | 360 | 270 | 243 | 267.3 |
| D | 450 | 472.5 | 519.75 | 415.8 | 519.75 |
| Total | 1350 | 1459.5 | 1416.75 | 1241.91 | 1467.97 |
Total closing values: Mon 1350, Tue 1459.5, Wed 1416.75, Thu 1241.91, Fri 1467.97. The lowest is on Thursday, when A, C and D all fell sharply (−25%, −10%, −20%).
Question 4
Numerical answer
A trader bought 10 shares of D at Monday's closing price and sold them at Wednesday's closing price. He then bought 10 shares of A at Thursday's closing price and sold them at Friday's closing price. What was his total profit (in ₹)?
Show answer and solution
Answer: 885.6
Closing prices (₹), computed by applying the successive changes:
| Stock | Mon | Tue | Wed | Thu | Fri |
|---|---|---|---|---|---|
| A | 220 | 209 | 250.8 | 188.1 | 206.91 |
| B | 380 | 418 | 376.2 | 395.01 | 474.01 |
| C | 300 | 360 | 270 | 243 | 267.3 |
| D | 450 | 472.5 | 519.75 | 415.8 | 519.75 |
| Total | 1350 | 1459.5 | 1416.75 | 1241.91 | 1467.97 |
D: bought at 450, sold at 519.75 → profit per share 69.75 → 10 shares: 697.5.
A: bought at 188.1, sold at 206.91 → profit per share 18.81 → 10 shares: 188.1.
Total profit = 697.5 + 188.1 = ₹885.6.
Tip: D from Mon close to Wed close changes by 1.05 × 1.1 = 1.155, i.e. +15.5% of 450 = 69.75; A on Friday gains 10% of 188.1 = 18.81.
| Stock | Mon | Tue | Wed | Thu | Fri |
|---|---|---|---|---|---|
| A | 220 | 209 | 250.8 | 188.1 | 206.91 |
| B | 380 | 418 | 376.2 | 395.01 | 474.01 |
| C | 300 | 360 | 270 | 243 | 267.3 |
| D | 450 | 472.5 | 519.75 | 415.8 | 519.75 |
| Total | 1350 | 1459.5 | 1416.75 | 1241.91 | 1467.97 |
D: bought at 450, sold at 519.75 → profit per share 69.75 → 10 shares: 697.5.
A: bought at 188.1, sold at 206.91 → profit per share 18.81 → 10 shares: 188.1.
Total profit = 697.5 + 188.1 = ₹885.6.
Tip: D from Mon close to Wed close changes by 1.05 × 1.1 = 1.155, i.e. +15.5% of 450 = 69.75; A on Friday gains 10% of 188.1 = 18.81.
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