Solve the following inequation and write the solution set

Q) By investing Rs. 45,000 in 10% Rs. 100 shares, Sharad gets Rs. 3,600 as dividend. Find the market value of each share.

Ans: Given values:

Investment = Rs. 45,000

Rate of dividend = 10%

Nominal value = Rs. 100

Annual dividend = Rs. 3,000

Step 1: Let market value of each share be X

Since the investment = 45,000 (given)

We know that, Investment = No. of shares x Market value of each share

∴ 45,000 = No. of shares (X)

∴ No. of shares invested or purchased = $\frac{45000}{\times}$

Step 2: Next, The Dividend Income earned = No. of shares × Nominal value of a share × Rate of Dividend

∴ 3600 = $\frac{45000}{\times}$ x 100 x 10% (from given values of Dividend amount, Nominal value and Rate of dividend)

∴ 360= $\frac{45000}{\times}$

∴ X= $\frac{45000}{360}$

∴ X= $\frac{500}{4}$

∴ X = 125

Therefore, the market value of each share is Rs. 125

Check: At 125/- share, no of shares bought for Rs 45,000

= $\frac{45000}{125}$ = 360 shares

Dividend earned on 360 shares of Rs. 100 @ 10% = 360 x 100 x 10% = 3600

Since it matches the value given in question, hence our answer is correct.

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