Meera holds shares of four listed companies – Alpha, Beta, Gamma and Delta. The dividend declared by a company is expressed as a percentage of the face value of its share; for example, a 20% dividend on a share of face value ₹10 means ₹2 per share. Meera's holdings did not change during 2016–2018. The table gives the face value, the number of shares Meera holds and the dividend declared each year; some entries are missing.
| Company | Face value (₹) | Shares held | Dividend 2016 | Dividend 2017 | Dividend 2018 |
|---|---|---|---|---|---|
| Alpha | 10 | 500 | 20% | 25% | 30% |
| Beta | 5 | 1,200 | 40% | ? | 50% |
| Gamma | 10 | ? | 15% | 15% | 20% |
| Delta | 2 | 2,000 | 100% | 125% | ? |
Meera's total dividend income from these four companies was ₹8,600 in 2016, ₹9,250 in 2017 and ₹12,100 in 2018.
The market prices per share at the beginning of 2018 were: Alpha ₹60, Beta ₹25, Gamma ₹40 and Delta ₹50. (Dividend yield = dividend per share ÷ market price.)
| Company | Face value (₹) | Shares held | Dividend 2016 | Dividend 2017 | Dividend 2018 |
|---|---|---|---|---|---|
| Alpha | 10 | 500 | 20% | 25% | 30% |
| Beta | 5 | 1,200 | 40% | ? | 50% |
| Gamma | 10 | ? | 15% | 15% | 20% |
| Delta | 2 | 2,000 | 100% | 125% | ? |
Meera's total dividend income from these four companies was ₹8,600 in 2016, ₹9,250 in 2017 and ₹12,100 in 2018.
The market prices per share at the beginning of 2018 were: Alpha ₹60, Beta ₹25, Gamma ₹40 and Delta ₹50. (Dividend yield = dividend per share ÷ market price.)
Question 1
Numerical answer
How many shares of Gamma does Meera hold?
Show answer and solution
Answer: 800
Dividend per share (₹) and income (₹):
- 2016: Alpha 2 × 500 = 1,000; Beta 2 × 1,200 = 2,400; Delta 2 × 2,000 = 4,000. Gamma = 8,600 − 7,400 = 1,200 → at ₹1.50 per share, Gamma holding = 800 shares.
- 2017: Alpha 1,250; Gamma 1,200; Delta 2.5 × 2,000 = 5,000. Beta = 9,250 − 7,450 = 1,800 → ₹1.50 per share = 30% of ₹5.
- 2018: Alpha 1,500; Beta 3,000; Gamma 2 × 800 = 1,600. Delta = 12,100 − 6,100 = 6,000 → ₹3 per share = 150% of ₹2.
| Company | 2016 | 2017 | 2018 |
|---|---|---|---|
| Alpha | 1,000 | 1,250 | 1,500 |
| Beta | 2,400 | 1,800 | 3,000 |
| Gamma | 1,200 | 1,200 | 1,600 |
| Delta | 4,000 | 5,000 | 6,000 |
| Total | 8,600 | 9,250 | 12,100 |
- 2016: Alpha 2 × 500 = 1,000; Beta 2 × 1,200 = 2,400; Delta 2 × 2,000 = 4,000. Gamma = 8,600 − 7,400 = 1,200 → at ₹1.50 per share, Gamma holding = 800 shares.
- 2017: Alpha 1,250; Gamma 1,200; Delta 2.5 × 2,000 = 5,000. Beta = 9,250 − 7,450 = 1,800 → ₹1.50 per share = 30% of ₹5.
- 2018: Alpha 1,500; Beta 3,000; Gamma 2 × 800 = 1,600. Delta = 12,100 − 6,100 = 6,000 → ₹3 per share = 150% of ₹2.
| Company | 2016 | 2017 | 2018 |
|---|---|---|---|
| Alpha | 1,000 | 1,250 | 1,500 |
| Beta | 2,400 | 1,800 | 3,000 |
| Gamma | 1,200 | 1,200 | 1,600 |
| Delta | 4,000 | 5,000 | 6,000 |
| Total | 8,600 | 9,250 | 12,100 |
Question 2
Single correct option
Based on the market prices at the beginning of 2018, which company offered Meera the highest dividend yield for 2018?
- A. Gamma
- B. Alpha
- C. Delta
- D. Beta
Show answer and solution
Answer: (D) Beta
Dividend per share (₹) and income (₹):
- 2016: Alpha 2 × 500 = 1,000; Beta 2 × 1,200 = 2,400; Delta 2 × 2,000 = 4,000. Gamma = 8,600 − 7,400 = 1,200 → at ₹1.50 per share, Gamma holding = 800 shares.
- 2017: Alpha 1,250; Gamma 1,200; Delta 2.5 × 2,000 = 5,000. Beta = 9,250 − 7,450 = 1,800 → ₹1.50 per share = 30% of ₹5.
- 2018: Alpha 1,500; Beta 3,000; Gamma 2 × 800 = 1,600. Delta = 12,100 − 6,100 = 6,000 → ₹3 per share = 150% of ₹2.
| Company | 2016 | 2017 | 2018 |
|---|---|---|---|
| Alpha | 1,000 | 1,250 | 1,500 |
| Beta | 2,400 | 1,800 | 3,000 |
| Gamma | 1,200 | 1,200 | 1,600 |
| Delta | 4,000 | 5,000 | 6,000 |
| Total | 8,600 | 9,250 | 12,100 |
2018 dividend per share ÷ price: Alpha 3/60 = 5%; Beta 2.5/25 = 10%; Gamma 2/40 = 5%; Delta 3/50 = 6%. Highest: Beta.
- 2016: Alpha 2 × 500 = 1,000; Beta 2 × 1,200 = 2,400; Delta 2 × 2,000 = 4,000. Gamma = 8,600 − 7,400 = 1,200 → at ₹1.50 per share, Gamma holding = 800 shares.
- 2017: Alpha 1,250; Gamma 1,200; Delta 2.5 × 2,000 = 5,000. Beta = 9,250 − 7,450 = 1,800 → ₹1.50 per share = 30% of ₹5.
- 2018: Alpha 1,500; Beta 3,000; Gamma 2 × 800 = 1,600. Delta = 12,100 − 6,100 = 6,000 → ₹3 per share = 150% of ₹2.
| Company | 2016 | 2017 | 2018 |
|---|---|---|---|
| Alpha | 1,000 | 1,250 | 1,500 |
| Beta | 2,400 | 1,800 | 3,000 |
| Gamma | 1,200 | 1,200 | 1,600 |
| Delta | 4,000 | 5,000 | 6,000 |
| Total | 8,600 | 9,250 | 12,100 |
2018 dividend per share ÷ price: Alpha 3/60 = 5%; Beta 2.5/25 = 10%; Gamma 2/40 = 5%; Delta 3/50 = 6%. Highest: Beta.
Question 3
Single correct option
By approximately what percentage did Meera's total dividend income increase from 2016 to 2018?
- A. 47.3%
- B. 35.2%
- C. 40.7%
- D. 30.8%
Show answer and solution
Answer: (C) 40.7%
Dividend per share (₹) and income (₹):
- 2016: Alpha 2 × 500 = 1,000; Beta 2 × 1,200 = 2,400; Delta 2 × 2,000 = 4,000. Gamma = 8,600 − 7,400 = 1,200 → at ₹1.50 per share, Gamma holding = 800 shares.
- 2017: Alpha 1,250; Gamma 1,200; Delta 2.5 × 2,000 = 5,000. Beta = 9,250 − 7,450 = 1,800 → ₹1.50 per share = 30% of ₹5.
- 2018: Alpha 1,500; Beta 3,000; Gamma 2 × 800 = 1,600. Delta = 12,100 − 6,100 = 6,000 → ₹3 per share = 150% of ₹2.
| Company | 2016 | 2017 | 2018 |
|---|---|---|---|
| Alpha | 1,000 | 1,250 | 1,500 |
| Beta | 2,400 | 1,800 | 3,000 |
| Gamma | 1,200 | 1,200 | 1,600 |
| Delta | 4,000 | 5,000 | 6,000 |
| Total | 8,600 | 9,250 | 12,100 |
(12,100 − 8,600)/8,600 × 100 = 3,500/8,600 × 100 ≈ 40.7%.
- 2016: Alpha 2 × 500 = 1,000; Beta 2 × 1,200 = 2,400; Delta 2 × 2,000 = 4,000. Gamma = 8,600 − 7,400 = 1,200 → at ₹1.50 per share, Gamma holding = 800 shares.
- 2017: Alpha 1,250; Gamma 1,200; Delta 2.5 × 2,000 = 5,000. Beta = 9,250 − 7,450 = 1,800 → ₹1.50 per share = 30% of ₹5.
- 2018: Alpha 1,500; Beta 3,000; Gamma 2 × 800 = 1,600. Delta = 12,100 − 6,100 = 6,000 → ₹3 per share = 150% of ₹2.
| Company | 2016 | 2017 | 2018 |
|---|---|---|---|
| Alpha | 1,000 | 1,250 | 1,500 |
| Beta | 2,400 | 1,800 | 3,000 |
| Gamma | 1,200 | 1,200 | 1,600 |
| Delta | 4,000 | 5,000 | 6,000 |
| Total | 8,600 | 9,250 | 12,100 |
(12,100 − 8,600)/8,600 × 100 = 3,500/8,600 × 100 ≈ 40.7%.
Question 4
Single correct option
In which year did the dividend from Beta form the smallest proportion of Meera's total dividend income?
- A. 2017
- B. 2018
- C. 2016
- D. It was the same in 2016 and 2018
Show answer and solution
Answer: (A) 2017
Dividend per share (₹) and income (₹):
- 2016: Alpha 2 × 500 = 1,000; Beta 2 × 1,200 = 2,400; Delta 2 × 2,000 = 4,000. Gamma = 8,600 − 7,400 = 1,200 → at ₹1.50 per share, Gamma holding = 800 shares.
- 2017: Alpha 1,250; Gamma 1,200; Delta 2.5 × 2,000 = 5,000. Beta = 9,250 − 7,450 = 1,800 → ₹1.50 per share = 30% of ₹5.
- 2018: Alpha 1,500; Beta 3,000; Gamma 2 × 800 = 1,600. Delta = 12,100 − 6,100 = 6,000 → ₹3 per share = 150% of ₹2.
| Company | 2016 | 2017 | 2018 |
|---|---|---|---|
| Alpha | 1,000 | 1,250 | 1,500 |
| Beta | 2,400 | 1,800 | 3,000 |
| Gamma | 1,200 | 1,200 | 1,600 |
| Delta | 4,000 | 5,000 | 6,000 |
| Total | 8,600 | 9,250 | 12,100 |
Beta's share: 2016: 2,400/8,600 ≈ 27.9%; 2017: 1,800/9,250 ≈ 19.5%; 2018: 3,000/12,100 ≈ 24.8%. Smallest in 2017 (the year Beta cut its dividend to 30%).
- 2016: Alpha 2 × 500 = 1,000; Beta 2 × 1,200 = 2,400; Delta 2 × 2,000 = 4,000. Gamma = 8,600 − 7,400 = 1,200 → at ₹1.50 per share, Gamma holding = 800 shares.
- 2017: Alpha 1,250; Gamma 1,200; Delta 2.5 × 2,000 = 5,000. Beta = 9,250 − 7,450 = 1,800 → ₹1.50 per share = 30% of ₹5.
- 2018: Alpha 1,500; Beta 3,000; Gamma 2 × 800 = 1,600. Delta = 12,100 − 6,100 = 6,000 → ₹3 per share = 150% of ₹2.
| Company | 2016 | 2017 | 2018 |
|---|---|---|---|
| Alpha | 1,000 | 1,250 | 1,500 |
| Beta | 2,400 | 1,800 | 3,000 |
| Gamma | 1,200 | 1,200 | 1,600 |
| Delta | 4,000 | 5,000 | 6,000 |
| Total | 8,600 | 9,250 | 12,100 |
Beta's share: 2016: 2,400/8,600 ≈ 27.9%; 2017: 1,800/9,250 ≈ 19.5%; 2018: 3,000/12,100 ≈ 24.8%. Smallest in 2017 (the year Beta cut its dividend to 30%).
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