A student gets 60 marks out of 80 in his first test and 70 marks out of 80 in his second test. Find the percentage increased in the 2nd test.
please help me.
Answers
Step-by-step explanation:
Answer:
Given :-
A student gets 60 marks out of 80 in his first test and 70 marks out of 80 in his second test.
To Find :-
What is the percentage increase in the second test.
Solution :-
\mapsto↦ In case of marks get out of 80 in his first test :
\implies⟹ 60 marks
\mapsto↦ In case of marks get out of 80 in his second test :
\implies⟹ 70 marks
Now, we have to find the total score percentage in the first and second test :
{\small{\bold{\purple{\underline{\bigstar\: In\: case\: of\: first\: test\: :-}}}}}
★Incaseoffirsttest:−
As we know that :
\begin{gathered}\longmapsto \sf\boxed{\bold{\pink{Total\: percentage\: scored =\: \dfrac{Total\: marks\: obtained}{Total\: marks} \times 100}}}\\\end{gathered}
⟼
Totalpercentagescored=
Totalmarks
Totalmarksobtained
×100
Given :
Total marks obtained = 60 marks
Total marks = 80 marks
According to the question by using the formula we get,
\begin{gathered}\leadsto \sf Total\: Percentage\: scored\: in\: {1}^{{st}}\: test\: =\: \dfrac{60}{8\cancel{0}} \times 10{\cancel{0}}\\\end{gathered}
⇝TotalPercentagescoredin1
st
test=
8
0
60
×10
0
\begin{gathered}\leadsto \sf Total\: Percentage\: scored\: in\: {1}^{{st}}\: test =\: \dfrac{60}{8} \times 10\\\end{gathered}
⇝TotalPercentagescoredin1
st
test=
8
60
×10
\begin{gathered}\leadsto \sf Total\: Percentage\: scored\: in\: {1}^{{st}}\: test =\: \dfrac{60 \times 10}{8}\\\end{gathered}
⇝TotalPercentagescoredin1
st
test=
8
60×10
\leadsto \sf Total\: Percentage\: scored\: in\: {1}^{{st}}\: test =\: \dfrac{\cancel{600}}{\cancel{8}}⇝TotalPercentagescoredin1
st
test=
8
600
\begin{gathered}\leadsto \sf\bold{\green{Total\: Percentage\: scored\: in\: {1}^{{st}}\: test =\: 75\%}}\\\end{gathered}
⇝TotalPercentagescoredin1
st
test=75%
Hence, the student scored 75% in the first test.
Again,
{\small{\bold{\purple{\underline{\bigstar\: In\: case\: of\: second\: test\: :-}}}}}
★Incaseofsecondtest:−
Given :
Total marks obtained = 70 marks
Total marks = 80 marks
According to the question by using the formula we get,
\begin{gathered}\leadsto\sf Total\: Percentage\: scored\: in\: {2}^{{nd}}\: test =\: \dfrac{70}{8\cancel{0}} \times 10{\cancel{0}}\\\end{gathered}
⇝TotalPercentagescoredin2
nd
test=
8
0
70
×10
0
\begin{gathered}\leadsto \sf Total\: Percentage\: scored\: in\: {2}^{{nd}}\: test =\: \dfrac{70}{8} \times 10\\\end{gathered}
⇝TotalPercentagescoredin2
nd
test=
8
70
×10
\begin{gathered}\leadsto \sf Total\: Percentage\: scored\: in\: {2}^{{nd}}\: test =\: \dfrac{70 \times 10}{8}\\\end{gathered}
⇝TotalPercentagescoredin2
nd
test=
8
70×10
\begin{gathered}\leadsto \sf Total\: Percentage\: scored\: in\: {2}^{{nd}}\: test =\: \dfrac{\cancel{700}}{\cancel{8}}\\\end{gathered}
⇝TotalPercentagescoredin2
nd
test=
8
700
\leadsto\sf\bold{\green{Total\: Percentage\: scored\: in\: {2}^{{nd}}\: test =\: 87.5\%}}⇝TotalPercentagescoredin2
nd
test=87.5%
Hence, the students scored 87.5% in the second test.
Now, we have to find the increase percentage in the second test :
So, we can write the formula as :
\begin{gathered}\longmapsto \sf\boxed{\bold{\pink{Increase\: percentage\: =\: Marks\: scored\: in\: {2}^{{nd}}\: test\: -\: Marks\: scored\: in\: {1}^{{st}}\: test}}}\\\end{gathered}
⟼
Increasepercentage=Marksscoredin2
nd
test−Marksscoredin1
st
test
Given :
Marks scored in second test = 87.5%
Marks scored in first test = 75%
According to the question by using the formula we get,
\begin{gathered}\dashrightarrow \sf Increase\: percentage =\: 87.5\% - 75\%\\\end{gathered}
⇢Increasepercentage=87.5%−75%
\begin{gathered}\dashrightarrow \sf Increase\: percentage =\: \dfrac{875}{10}\% - 75\%\\\end{gathered}
⇢Increasepercentage=
10
875
%−75%
\begin{gathered}\dashrightarrow \sf Increase\: percentage =\: \bigg(\dfrac{875}{10} - 75\bigg)\%\\\end{gathered}
⇢Increasepercentage=(
10
875
−75)%
\begin{gathered}\dashrightarrow\sf Increase\: percentage =\: \bigg(\dfrac{875 - 750}{10}\bigg)\%\\\end{gathered}
⇢Increasepercentage=(
10
875−750
)%
\begin{gathered}\dashrightarrow \sf Increase\: percentage =\: \bigg(\dfrac{125}{10}\bigg)\%\\\end{gathered}
⇢Increasepercentage=(
10
125
)%
\begin{gathered}\dashrightarrow \sf\bold{\red{Increase\: percentage =\: 12.5\%}}\\\end{gathered}
⇢Increasepercentage=12.5%
\therefore∴ The increase percentage that students gets in the second test is 12.5%.