Question
Meera spends 30% of her income on house rent and then
uses 25% of the remaining money on groceries. From what is left, she deposits 40% in her bank. The rest she invests in mutual funds and bonds in the ratio 7:3. If the difference between the amounts invested in mutual funds and bonds is Rs. 12,600, find the amount deposited in the bank by Meera.Solution
ATQ, Let Meera’s income be Rs. ‘100x’ Rent = 100x × 0.30 = Rs. ‘30x’ Remaining = 100x − 30x = Rs. ‘70x’ Groceries = 70x × 0.25 = Rs. ‘17.5x’ Remaining = 70x − 17.5x = Rs. ‘52.5x’ Bank deposit = 52.5x × 0.40 = Rs. ‘21x’ Remaining = 52.5x − 21x = Rs. ‘31.5x’ Investment split = 7 : 3 (total parts = 10) Mutual funds = 31.5x × (7/10) = Rs. ‘22.05x’ Bonds = 31.5x × (3/10) = Rs. ‘9.45x’ ATQ; Difference = 22.05x − 9.45x = 12.6x = 12600 So, ‘x’ = 12600 / 12.6 = 1000 Hence, bank deposit = Rs. ‘21x’ = 21 × 1000 = Rs. 21,000
The coefficient of correlation between two variables X and Y is 0.6 .
The covariance between X and Y is 30 .
The variance of X is 25 .
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