Stocks A, B and C are priced at rupees 120, 90 and 150 per share, respectively. A trader holds a portfolio consisting of 10 shares of stock A, and 20 shares of stocks B and C put together. If the total value of her portfolio is rupees 3300, then the number of shares of stock B that she holds, is

The correct answer is 15.

Let the number of shares of stock A, B, and C be denoted as n_A, n_B, and n_C respectively. We are given the following prices per share:

$\text{Price of A}=120$

$\text{Price of B}=90$

$\text{Price of C}=150$

We are told that the trader holds 10 shares of stock A. Therefore, the total value of the shares of stock A in the portfolio is:

$10\times 120=1200$

The total value of the entire portfolio is given as 3300. This means the combined value of the shares of stock B and C must be the total portfolio value minus the value of the shares of stock A:

$3300-1200=2100$

We are also given that the total number of shares of stock B and stock C put together is 20. Thus, we can write an equation for the number of shares of stock C in terms of the number of shares of stock B:

$n_B+n_C=20$

$n_C=20-n_B$

Now we can set up an equation for the combined value of stocks B and C. The value is the number of shares of stock B times its price plus the number of shares of stock C times its price:

$90n_B+150n_C=2100$

Substitute our expression for n_C into this equation:

$90n_B+150(20-n_B)=2100$

Expand the expression on the left side:

$90n_B+3000-150n_B=2100$

Combine the n_B terms together:

$3000-60n_B=2100$

Subtract 3000 from both sides:

$-60n_B=2100-3000$

$-60n_B=-900$

Divide both sides by -60 to solve for the number of shares of stock B:

$n_B=\frac{-900}{-60}$

$n_B=15$

Therefore, the number of shares of stock B that she holds is 15.