Question

In a class test, the sum of the marks obtained by P in mathematics and
science is 28. Had he got 3 more marks in mathematics and 4 marks less
in science, the product of marks obtained in the two subjects would
have been 180. Find the marks obtained by him in the two subjects
separately.​

Answer 1

Answer:

$\begin{gathered}\boxed{\begin{array}{c|c} \sf Marks\:obtained\:in\:maths & \sf Marks\:obtained\:in\:science \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 9 & \sf 19 \\ \\ \sf 12 & \sf 16 \end{array}} \\ \end{gathered}$

Step-by-step explanation:

Given that, marks obtained by P in mathematics and science is 28.

Let assume that

$\boxed{\begin{aligned}&\:\sf \:Marks\:obtained\:in\:maths=x \: \\ \\& \:\sf \: Marks\:obtained\:in\:science=28 -x \end{aligned}} \qquad \:$

Further given that, had he got 3 more marks in maths and 4 marks less in science, the product of marks obtained in the two subject would have been 180.

So, we have

$\boxed{\begin{aligned}&\:\sf \:Marks\:obtained\:in\:maths=x + 3 \: \\ \\& \:\sf \: Marks\:obtained\:in\:science=28 -x - 4 = 24 - \end{aligned}} \qquad \:$

According to statement, we get

$\sf \: (x + 3)(24 - x) = 180$

$\sf \: 24x - {x}^{2} + 72 - 3x = 180$

$\sf \: 21x - {x}^{2} + 72 = 180$

$\sf \: {x}^{2} - 21x + 108 = 0$

$\sf \: {x}^{2} - 9x - 12x+ 108 = 0$

$\sf \: x(x - 9) - 12(x - 9) = 0$

$\sf \: (x - 9)(x - 12) = 0$

$\implies\sf \: x = 9 \: \: or \: \: x = 12$

Hence,

$\begin{gathered}\boxed{\begin{array}{c|c} \sf Marks\:obtained\:in\:maths & \sf Marks\:obtained\:in\:science \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 9 & \sf 19 \\ \\ \sf 12 & \sf 16 \end{array}} \\ \end{gathered}$

Answer 2

Step-by-step explanation:

Hope this helps you!!!!!!!