# In a class test $(+3)$ marks are given for every correct answer and $(-2)$ marks are given for every incorrect answer and no marks for not attempting any question.(i) Radhika scored $20$ marks. If she has got $12$ correct answers, how many questions has she attempted incorrectly?(ii) Mohini scores $-5$ marks in this test, though she has got $7$ correct answers. How many questions has she attempted incorrectly?

Given :

Marks given for every correct answer $= +3$

Marks given for every incorrect answer $= -2$

Number of marks scored by Radhika $=20$ marks

Correct answers by Radhika $= 12$

Number of marks scored by Mohini $=-5$ marks

Correct answers by Mohini $= 7$

To do:

We have to find the number of questions incorrectly attempted by (i) Radhika (ii) Mohini.

Solution :

(i) Marks given for correct answers for Radhika $= 12 \times (+3) = 36$

Marks given for incorrect answers $=$ Number of marks scored by Radhika $-$ Marks given for correct answers

$=20-36$

$=-16$

This implies,

The number of questions incorrectly attempted by Radhika $=-16 \div (-2)$

$=-16\times (\frac{1}{-2})$

$=8$

(ii) Marks given for correct answers for Mohini $= 7 \times (+3) = 21$

Marks given for incorrect answers $=$ Number of marks scored by Mohini  $-$ Marks given for correct answers

$=-5-21$

$=-26$

This implies,

The number of questions incorrectly attempted by Mohini $=-26 \div (-2)$

$=-26\times (\frac{1}{-2})$

$=13$

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