Question

A boy set 3 marks of each correct sum and lose 2 marks of each incorrect sums he does 24 sums and obtained 37 marks the number of correct sums were

Answer 1

Correct Question:-

A boy get 3 marks of each correct sum and lose 2 marks of each incorrect sums, he does 24 sums and obtained 37 marks. Find the number of correct sums.

Answer:-

The number of correct sums is 17.

Given:

• A boy get 3 marks of each correct sum and lose 2 marks of each incorrect sums, he does 24 sums.

• He obtained 37 marks.

To find:

• Number of correct sums.

Solution:-

Let the number of correct sums be x and incorrect sums be y.

According to the first condition.

=> x+y=24...(1)

According to the second condition.

=> 3x-2y=37...(2)

Multiply equation (1) by 2, we get

=> 2x+2y=48...(3)

Add equations (2) and (3), we get

3x-2y=37

+

2x+2y=48

__________

5x=85

$\sf{\therefore{x=\frac{85}{5}}}$

$\sf{\therefore}$ x=17

$\sf{\therefore}$ The number of correct sums is 17.

Answer 2

$\purple{\underline{\underline{\pink{\boxed{\boxed{\red{\star{\sf Question:}}}}}}}}$

$\rm{A \ boy \ set \ 3 \ marks \ of \ each \ correct \ sum }$

$\rm{and \ lose \ 2 \ marks \ of \ each \ incorrect \ sums}$

$\rm{he \ does \ 24 \ sums \ and \ obtained \ 37 \ marks. }$

$\rm{What \ is \ number \ of \ correct \ sums }$

_________________________________________

$\purple{\underline{\underline{\orange{\boxed{\boxed{\green{\star{\sf Answer:}}}}}}}}$

$\rm{\blue{\boxed{\red{Number \ of \ correct \ sums \ : \ 17}}}}$

_________________________________________

$\sf\large\underline\pink{Given:}$

$\rm\longrightarrow{A \ boy \ get \ 3 \ marks \ of \ each}$

$\rm{ correct \ sum \ and \ lose \ 2 \ marks \ of \ each}$

$\rm\longrightarrow{ incorrect sums, he does 24 sums.}$

$\rm\longrightarrow{He \ obtained \ 37 \ marks.}$

_________________________________________

$\sf\large\underline\blue{To \ Find}$

$\rm{Number \ of \ correct \ sums}$

_________________________________________

$\green{\underline{\underline{\red{\boxed{\boxed{\purple{\star{\sf Solution:}}}}}}}}$

$\rm{Let \ the \ number \ of \ correct \ sums \ be \ m}$

$\rm{and \ the \ number \ of \ incorrect \ ones \ be \ n.}$

$\rm{Then, \ according \ to \ the \ question}$

$\rm{As, \ he \ attempted \ 24 \ questions \ in \ total}$

$\rm\implies{m+n=24 ...........(a)}$

$\rm{he \ gets \ 3 \ marks \ for \ correct \ sum}$

$\rm{ and \ loses \ 2 \ marks \ for \ wrong \ sum}$

$\rm\implies{3m-2n=37.........(b)}$

$\rm{Multiplying \ (a) \ by \ 2 \ and \ adding \ it \ to \ (b).}$

$\rm\implies{2m \ + \ 2n \ + \ 3m \ -\ 2n \ = \ 48 \ + \ 37}$

$\rm\implies{5m=85}$

$\rm\therefore{\green{\boxed{\orange{m=17}}}}$

$\rm{From \ equation \ (a)}$

$\rm\implies{17+n=24}$

$\rm\implies{n=24-17}$

$\rm\therefore{\green{\boxed{\orange{n=7}}}}$

$\rm\therefore{He \ did \ 17 \ correct \ sums.}$

$\rm{\blue{\boxed{\red{Number \ of \ correct \ sums \ : \ 17}}}}$

___________________________________________

$\rm\orange{Hope \ it \ helps \ :))}$