Question

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.​

Answer 1

Answer:

12.5%

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Step-by-step explanation:

Method 1: Finding the % scored in each test, and then subtracting them.

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According to the question;

• Marks scored out of 80 in the 1st test = 60.

• Marks scored out of 80 in the 2nd test = 70.

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The scores in percentage will be;

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First test:

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$\sf \dashrightarrow \% \ Scored \ in \ the \ first \ test = \dfrac{Score \ Obtained}{Total \ Score} \times 100$

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$\sf \dashrightarrow \% \ Scored \ in \ the \ first \ test = \dfrac{60}{80} \times 100$

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$\sf \dashrightarrow \% \ Scored \ in \ the \ first \ test = \dfrac{6}{8} \times 100$

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$\sf \dashrightarrow \% \ Scored \ in \ the \ first \ test = 0.75 \times 100$

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$\sf \dashrightarrow \% \ Scored \ in \ the \ first \ test = \bold{75 \%}$

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Second test:

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$\sf \dashrightarrow \% \ Scored \ in \ the \ second \ test = \dfrac{Score \ Obtained}{Total \ Score} \times 100$

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$\sf \dashrightarrow \% \ Scored \ in \ the \ second \ test = \dfrac{70}{80} \times 100$

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$\sf \dashrightarrow \% \ Scored \ in \ the \ second \ test = \dfrac{7}{8} \times 100$

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$\sf \dashrightarrow \% \ Scored \ in \ the \ second \ test = 0.875 \times 100$

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$\sf \dashrightarrow \% \ Scored \ in \ the \ second \ test = \bold{87.5 \%}$

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Therefore;

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% Increase = % Scored in the 2nd test - % Scored in the 1st test

% Increase = 87.5 % - 75 %

% Increase = 12.5

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Method 2: Using the % Increase formula.

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$\sf \dashrightarrow \% \ Increase = \dfrac{Difference \ in \ score}{Total \ Score} \times 100$

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$\sf \dashrightarrow \% \ Increase = \dfrac{Score \ in \ the \ 2nd \ test - Score \ in \ the \ 1st \ test}{Total \ Score} \times 100$

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$\sf \dashrightarrow \% \ Increase = \dfrac{70 - 60}{80} \times 100$

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$\sf \dashrightarrow \% \ Increase = \dfrac{10}{80} \times 100$

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$\sf \dashrightarrow \% \ Increase = 0.125 \times 100$

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$\sf \dashrightarrow \ \bold{\% \ Increase = 12.5}$

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Hence solved.

Answer 2

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 :

${\small{\bold{\purple{\underline{\bigstar\: In\: case\: of\: first\: test\: :-}}}}}$

As we know that :

$\longmapsto \sf\boxed{\bold{\pink{Total\: percentage\: scored =\: \dfrac{Total\: marks\: obtained}{Total\: marks} \times 100}}}$

Given :

• Total marks obtained = 60 marks
• Total marks = 80 marks

According to the question by using the formula we get,

$\leadsto \sf Total\: Percentage\: scored\: in\: {1}^{{st}}\: test\: =\: \dfrac{60}{8\cancel{0}} \times 10{\cancel{0}}$

$\leadsto \sf Total\: Percentage\: scored\: in\: {1}^{{st}}\: test =\: \dfrac{60}{8} \times 10$

$\leadsto \sf Total\: Percentage\: scored\: in\: {1}^{{st}}\: test =\: \dfrac{60 \times 10}{8}$

$\leadsto \sf Total\: Percentage\: scored\: in\: {1}^{{st}}\: test =\: \dfrac{\cancel{600}}{\cancel{8}}$

$\leadsto \sf\bold{\green{Total\: Percentage\: scored\: in\: {1}^{{st}}\: test =\: 75\%}}$

Hence, the student scored 75% in the first test.

Again,

${\small{\bold{\purple{\underline{\bigstar\: In\: case\: of\: second\: test\: :-}}}}}$

Given :

• Total marks obtained = 70 marks
• Total marks = 80 marks

According to the question by using the formula we get,

$\leadsto\sf Total\: Percentage\: scored\: in\: {2}^{{nd}}\: test =\: \dfrac{70}{8\cancel{0}} \times 10{\cancel{0}}$

$\leadsto \sf Total\: Percentage\: scored\: in\: {2}^{{nd}}\: test =\: \dfrac{70}{8} \times 10$

$\leadsto \sf Total\: Percentage\: scored\: in\: {2}^{{nd}}\: test =\: \dfrac{70 \times 10}{8}$

$\leadsto \sf Total\: Percentage\: scored\: in\: {2}^{{nd}}\: test =\: \dfrac{\cancel{700}}{\cancel{8}}$

$\leadsto\sf\bold{\green{Total\: Percentage\: scored\: in\: {2}^{{nd}}\: test =\: 87.5\%}}$

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 :

$\longmapsto \sf\boxed{\bold{\pink{Increase\: percentage\: =\: Marks\: scored\: in\: {2}^{{nd}}\: test\: -\: Marks\: scored\: in\: {1}^{{st}}\: test}}}$

Given :

• Marks scored in second test = 87.5%
• Marks scored in first test = 75%

According to the question by using the formula we get,

$\dashrightarrow \sf Increase\: percentage =\: 87.5\% - 75\%$

$\dashrightarrow \sf Increase\: percentage =\: \dfrac{875}{10}\% - 75\%$

$\dashrightarrow \sf Increase\: percentage =\: \bigg(\dfrac{875}{10} - 75\bigg)\%$

$\dashrightarrow\sf Increase\: percentage =\: \bigg(\dfrac{875 - 750}{10}\bigg)\%$

$\dashrightarrow \sf Increase\: percentage =\: \bigg(\dfrac{125}{10}\bigg)\%$

$\dashrightarrow \sf\bold{\red{Increase\: percentage =\: 12.5\%}}$

$\therefore$ The increase percentage that students gets in the second test is 12.5%.