Mathematics
₹ 40 is distributed between two friends such that the product of their shares is 364. The difference of their shares is:
₹ 8
₹ 10
₹ 12
₹ 14
Answer
Given,
The total amount of money = ₹ 40.
Let the shares of two friends be ₹ x and ₹ y respectively.
⇒ x + y = 40
⇒ y = 40 - x ………(1)
Given,
The product of two parts of amount distributed is 364.
⇒ xy = 364 ………(2)
Substituting value of y from equation (1) in equation (2), we get :
⇒ x(40 - x) = 364
⇒ 40x - x2 = 364
⇒ x2 - 40x + 364 = 0
⇒ x2 - 26x - 14x + 364 = 0
⇒ x(x - 26) - 14(x - 26) = 0
⇒ (x - 14)(x - 26) = 0
⇒ (x - 14) = 0 or (x - 26) = 0 [Using zero-product rule]
⇒ x = 14 or x = 26
Substituting value of x in equation (1), we get:
Case 1: If x = 14, y = 40 − 14 = 26
Case 2: If x = 26, y = 40 − 26 = 14.
The difference between the two parts of amount is, ₹ 26 - ₹ 14 = ₹ 12.
Hence, option 3 is the correct option.
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