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371.
A takes 6 days less than B to do a work. If both A and B working together can do it in 4 days, how many days will B take to finish it?

Suppose B alone takes x days to to finish the work.

Then, A alone can finish it in (x-6) days.

(A's one days work) + (B's one day work) = $\frac{1}{x - 6} + \frac{1}{x}$

And, ( A+B)'s one day's work = $\frac{1}{4}$

$∴ \frac{1}{x - 6} + \frac{1}{x} = \frac{1}{4} \Rightarrow \frac{x + x - 6}{x (x - 6)} = \frac{1}{4} \Rightarrow \frac{2 x - 6}{x^{2} - 6 x} = \frac{1}{4} \Rightarrow 8 x - 24 = x^{2} - 6 x \Rightarrow x^{2} - 6 x - 8 x + 24 = 0 \Rightarrow x^{2} - 14 x + 24 = 0 \Rightarrow x^{2} - 12 x - 2 x + 24 = 0 \Rightarrow x (x - 12) - 2 (x - 12) = 0 \Rightarrow (x - 12) (x - 2) = 0 \Rightarrow x - 12 = 0 or x - 2 = 0 \Rightarrow x = 12 or x = 2$

But, x cannot be less than 6.

So, x = 12

Hence, B alone can finish the work in 12 days.

Multiple Choice Questions

372.

If 1 is a root of the equations ay2 + ay + 3 = 0 and y2 + y + b = 0, then ab equals

3
$- \frac{7}{2}$
6
-3

Long Answer Type

373.

Find the values (s) of k so that the quadratic equation 3x² - 2kx + 12 = 0 has equal roots.

374.

Solve for x: 4x² – 4ax + (a² – b²) = 0

Solve for x: 3x² - $\sqrt{6}$ x + 2 = 0

375.

A shopkeeper buys some books for Rs. 80. If he had bought 4 more books for the same amount, each book would have cost Rs. 1 less. Find the number of books he bought.

The sum of two number is 9 and the sum of their reciprocals is $\frac{1}{2}$ . Find the numbers.