Question

1/A+1/B=1/35 and 4A/7+3B/7=114 then find A and B?​

Answer 1

Answer:

Let us assume that A completes the work alone in X number of days.

Work done by A and B in 1 day = 1/35 (given)

Work done by A alone in 1 day = 1/X

Work done by B alone in 1 day = (1/35) - (1/X) = (X - 35) / 35X

No. Of days taken by A for doing 5/7 of work = (5/7) / (1/X) = 5X/7 days.

No. Of days taken by B for doing remaining 2/7 of work = (2/7) / {(X - 35) / 35X}

= 70X / 7(X - 35) = 10X / (X - 35) days

Therefore,

(5X/7) + {10X / (X - 35)} = 90 days (given)

Rearranging the equation we get,

5X(X-35) + 70X = 630 (X - 35)

Or 5 X^2 - 175X + 70X = 630X + 22050

Or X^2 - 147X + 4410 = 0

Solving for X,

(X - 105) (X - 42) = 0

It can be seen that X can not be 42.

So X must be 105 days.

Ans. A alone can finish the work in 105 days.

It can be shown that B alone can do the work in 52.5 days.

Verification:

A does 5/7 of work in (105*5/7) = 75 days.

B does the remaining work of 2/7 in (52.5*2/7) = 15 days.

So total number of days = 90.

Answer 2

The values of A and B are 166.26 and 42.33 respectively.

Step-by-step explanation:

According to the given information, the equations are given as,

$\frac{1}{A} + \frac{1}{B} = \frac{1}{35}$ and $\frac{4A}{7} + \frac{3B}{7} = 114$.

Now, in order to get the final values of A and B, we need to solve the simultaneous linear equations.

Now, starting with the first equation, that is,

$\frac{1}{A} + \frac{1}{B} = \frac{1}{35}$,

Multiplying AB on both sides of the equation for simplification, we get,

$\frac{AB}{A} +\frac{AB}{B}=\frac{AB}{35}$

Now, cancelling A and B from the individual terms, we get, the equation as,

35*(B+A) = AB

Or, 35 A + 35 B = AB

Or, 35 A + 35B - AB = 1

Or, 35A + B(35-A) = 1

Or, B(35-A) = 1-35A

Or, B = $\frac{1-35A}{35-A}$

Let us suppose this equation is equation (1).

Now, let us consider the second given equation, that is,

$\frac{4A}{7} + \frac{3B}{7} = 114$

This gives, 4A + 3B = 7*114

That is, 4A+3B = 798

Let us suppose this is equation (2).

Now, putting the value of B from equation (1) in equation (2), we get,

4A+3($\frac{1-35A}{35-A}$) = 798

$Or, 4A(35-A) +3(1-35A) = 798(35-A)\\Or, 140A-4A^{2} +3-105A = 27930 - 798A\\Or, 4A^{2} -140A+105A-798A-3+27930 = 0\\Or, 4A^{2} -833A+27927=0$

Thus, A  = 166.26

Now, putting this value of A in (1), we get,

B =

$\frac{1-35(166.26)}{35-166.26} \\=42.33$

Thus, B = 42.33

Hence, the values of A and B are 166.26 and 42.33 respectively.

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