Question

Let P(a,b,c,d)=2a + 3bc + 4c^2d. If a, b, c and d are increased by 80%, 50%, 20% and 25% Tespectively,
find what is the per cent increase in P(a,b,c,d).​

Answer 1

Answer:

Let P(a,b,c,d)=2a + 3bc + 4c^2d. If a, b, c and d are increased by 80%, 50%, 20% and 25% Tespectively,

find what is the per cent increase in P(a,b,c,d).

Answer 2

Answer:

The percentage increase in P(a,b,c,d) is 80%

Step-by-step explanation:

Assuming the equation  to be:

$P(a,b,c,d)= 2a+3bc+4c^{2}d$

As per the question,

• a increased by 80% ⇒ 1.8a

• b increased by 50% ⇒ 1.5b

• c increased by 20% ⇒ 1.2c

• d increased by 25% ⇒ 1.25d

Percent increase in P(a,b,c,d) is found by substituting the increased values in the function

$P(a,b,c,d)= 2a+3bc+4c^{2}d$ -------(1)

∴

$P_{1} (a,b,c,d)$  ⇒  $2\times 1.8a + 3\times 1.5b\times1.2c+4\times1.2^{2} c^{2} \times 1.25d$

⇒ $3.6a+ 5.4bc+ 7.2c^{2}d$ --------(2)

If we substitute a=b=c=d=1 in equation (1) and (2),

P(a,b,c,d) = 9

and

$P_{1} (a,b,c,d)$ = 16.2

Percentage increase = $\frac{16.2- 9}{9}\times 100$

=$\frac{7.2}{9}\times 100$

= 80 %

The correct answer is 80%