Question

A man invests Rs. 6750, partly in a share of 6% at Rs 140 and partly in a share of 5% at RS 125. If his total income is Rs. 280, how much has he invested in each?

Answer 1

Hint: The given problem is based on the concept of shares. We can calculate the total investment by taking the difference of investment in both the cases. Further we can calculate the investment in each case by using the formula \[income = \dfrac{{dividend\% }}{{Cost{\text{ }}of{\text{ }}one{\text{ }}share}} \times investment\] .

Complete step by step solution:
Let us assume that the investment of the man in shares paying 6% at ₹140 be \[x\]
Then his investment in shares paying 5% at ₹125 \[ = \left( {6750 - x} \right)\]
Now for the first share the income can be calculate using the formula \[income = \dfrac{{dividend\% }}{{Cost{\text{ }}of{\text{ }}one{\text{ }}share}} \times investment\]
Now dividend given for the first share is \[6\% \] and the cost of one share is 140 on substituting these values in the above formula we get
 \[income = \left( {\dfrac{6}{{140}} \times x} \right)\]
 \[income = \dfrac{{3x}}{{70}} - - - (1)\]
In the question given that Income on one share of Rs. \[125\] = Rs. \[5\]
Now dividend given for the first share is \[5\% \] and the cost of one share is 125 on substituting these values in the above formula we get
Income on Rs. \[(6750 - x)\] =
 \[ \Rightarrow \dfrac{{6750 - x}}{{125}} \times 5\]
 \[ \Rightarrow Rs.\dfrac{1}{{25}}(6750 - x) - - - (2)\]
Now adding the two incomes and given that the total income is Rs. \[280\]
 \[ \Rightarrow \dfrac{{3x}}{{70}} + \dfrac{{6750 - x}}{{25}} = 280\]
 \[ \Rightarrow \dfrac{{15x + 14 \times 6750 - 14x}}{{350}} = 280\]
 \[ \Rightarrow x + 14 \times 6750 = 280 \times 350\]
 \[\Rightarrow x = 3500\]
 \[6750 - x = 6750 - 3500\]
 \[ = 3250\]
Investment in paying shares \[6\% \] at Rs. \[140\] is Rs. \[3500\]
 \[\therefore \] Investment in paying shares \[5\% \] at Rs. \[125\] is Rs.$3250$

Note: On dividing the whole or a group of objects into equal parts, we get equal shares. We need to divide an object or a whole number into equal parts to distribute it equally. These equal parts have to be the same in measurements like weight, volume, dimensions, numbers etc.