Algebra

Linear Equation

Medium

An examination consists of 160 questions. One mark is given for every correct option. If a 1/4 mark is deducted for each wrong option and a half mark is deducted for each unanswered question, then a student scores 79. If half a mark is deducted for every wrong option and 1/4 mark is deducted for every unanswered question, the same student scores 76. Find the number of correct answers he wrote.

140

100

120

✅ Correct Option: 3

Let $c$ = correct answers, $w$ = wrong answers, $u$ = unanswered questions.

$c + w + u = 160 \quad \text{...(i)}$

From the two scoring schemes:

$c - \dfrac{w}{4} - \dfrac{u}{2} = 79 \quad \text{...(ii)}$

$c - \dfrac{w}{2} - \dfrac{u}{4} = 76 \quad \text{...(iii)}$

Subtracting (iii) from (ii):

$\dfrac{w}{4} - \dfrac{u}{4} = 3$

$w - u = 12 \quad \text{...(iv)}$

Adding (ii) and (iii):

$2c - \dfrac{3w}{4} - \dfrac{3u}{4} = 155$

$2c - \dfrac{3}{4}(w + u) = 155$

From (i), $w + u = 160 - c$

$2c - \dfrac{3}{4}(160 - c) = 155$

$2c - 120 + \dfrac{3c}{4} = 155$

$\dfrac{11c}{4} = 275$

$c = 100$

The number of correct answers $= 100$

BMSAT Kozhikode 2025

A told B, “When I was as old as you are now, then your age was four years less than half of my present age". If the sum of the present ages of A and B is 61 years, what is B's present age in years?

BMSAT Kozhikode 2026

Runs scored by Sachin in a charity match are 10 more than the balls faced by Lara. The number of balls faced by Sachin is 5 less than the runs scored by Lara. Together, they have scored 105 runs and Sachin faced 10 balls less than the balls faced by Lara. How many runs were scored by Sachin?

BMSAT Kozhikode 2026

If the breadth of a rectangle is increased by 5 cms, its area is increased by 25 sq.cm. If the length is increased by 5 cms, its area increases by 20 sq.cm. Find the area of the rectangle in sq.cm.

BMSAT Kozhikode 2026

Navin got 60% of the maximum marks in his college's exam for his batch but missed that year's 'Deans List' threshold by 60 marks. His batchmate Pravin scored 80% of the maximum, and this score was 40 marks more than the same threshold. What was that year's 'Deans List' threshold?

Solution

Related questions:

Keyboard Shortcuts

BMSAT Kozhikode Past Year Questions (Topic-Wise)