Question

When A increases by 8%, then B increases by 6%, and when B increases by 8%, then Cincreases by 4%
A is increased from 12 to 18. C must, therefore, increase from 30 to:​

Answer 1

Answer:

35.625

Step-by-step explanation:

Given,

If A increases by 8%, then B increases by 6%,

So, the ratio in percentage increases in A and percentage increases in B = $\frac{8}{6}$ = $\frac{4}{3}$

Let percentage increases in A = 4x and percentage increases in B = 3x,

Where, x is any positive real number,

Now, if B increases by 8%, then C increases by 4%,

So, the ratio  in percentage increases in B and C = $\frac{8}{4}$ $=\frac{2}{1}$

Let percentage increases in B = 2y and percentage increases in C = y,

Where, y is any positive real number,

$\implies 2y = 3x\implies y = \frac{3x}{2}$

Hence,

$\frac{\text{Percentage increases in A}}{\text{Percentage increase in C}}=\frac{4x}{3x/2}=\frac{8x}{3x}=\frac{8}{3}----(1)$

∵ A is increased from 12 to 18,

$\implies \text{Percentage increase in A}=\frac{18-12}{12}\times 100=\frac{6}{12}\times 100=50\%$

From equation (1),

$\frac{50}{\text{Percentage increase in C}}=\frac{8}{3}$

$\implies \text{Percentage increase in C}=\frac{3\times 50}{8}=\frac{150}{8}\%$

Finally,

If Initial value of C = 30,

Then new value of C after increasing 150/8%

$=\frac{30(100+\frac{150}{8})}{100}$

$=\frac{30\times 950}{800}$

$=35.625$

Answer 2

Answer:

35.625

Step-by-step explanation:

Given:- When A increases by 8%, B increases by 6%.

             When B increases by 8%, C increases by 4%.

To Find:- Increase in C when A is increases from 12 to 18.

Solution:-

As given, B increases by 6% when A increases by 8%.

∴ Ratio of percentage increases in A and B = 8/6 = 4/3.

Let the percentage increase in A be 4x and in B be 3x.

Now, Ration of percentage increase in B and C = 8/4 = 2/1

Let the percentage increase in B be 2y and in C be y.

From the above statement we can derive that

                                3x = 2y

                            ⇒ y = 3x/2.

Hence, $\frac{Percentage increase in A}{Percentage increase in C} = \frac{4x}{y}$              -------- ( 1 )

                                             $= \frac{4x}{\frac{3x}{2} }$   $= \frac{8}{3}$

As A increases from 12 to 18,

∴ Percentage increase in A = $\frac{18 - 12}{12} * 100$

                                              = $\frac{6}{12} * 100$

                                             = 50%

Putting this in equation ( 1 )

Percentage increase in C = (3 × 50)/8        

                                           = 150/8%

The value of C after increasing $\frac{150}{8}$% is

⇒ $\frac{150}{8}$ = $\frac{value - 30}{30} * 100$

⇒ $value - 30 = \frac{150 * 3}{80}$

⇒ $value = \frac{45}{8} + 30$

⇒ $value = \frac{45 + 240}{8}$

⇒ $value = \frac{285}{8}$

⇒ value = 35.625

Therefore, C increases from 30 to 35.625.

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