Question

A person invested 20%, 30% and 25% of his saving in buying shares at par values of three different companies A, B and C which declare dividends of 10%, 12% and 15%, respectively. If his total income on account of dividends be ₹ 4,675, find his saving and the amount which he invested in buying shares of each company.

Answer 1

Given:

20% of savings in Company A (10% dividend)

30% of savings in Company B (12% dividend)

25% of savings in Company C (15% dividend)

Total dividend income = ₹ 4675

Investment in A = 20% of x `= (20x)/100 = x/5`

Investment in B = 30% of x `= (30x)/100 = (3x)/10`

Investment in C = 25% of x `= (25x)/100 = x/4`

Calculate dividend income from each company

Company A: 10% of `x/5 = 10/100 xxx/5`

Company B: 12% of `(3x)/10 = 12/100 xx(3x)/10 = (36x)/1000 = (9x)/250`

Company C: 15% of `x/4 = 15/100 xx x/4 = (3x)/80`

`x/50 + (9x)/250 + (3x)/80 = 4675`

Convert all to common denominator:

`x/50 = (80x)/4000`

`(9x)/250 = (144x)/4000`

`(3x)/80 = (150x)/4000`

`=> (80x + 144x + 150x)/4000`

= 4675

`=> (374x)/4000`

= 4675

374x = 4675 × 4000

= 18,700,000

`=>x = 18700000/374`

= ₹ 50,000

Total savings = ₹ 50,000

Investment in Company A = ₹ 10,000

Investment in Company B = ₹ 15,000

Investment in Company C = ₹ 12,500