Question

2. An examination was conducted
for 1200 marks. A scored 25%
more than B and B secured 20%
more than C. C scored 20% less
than D. If A secured 960 marks,
what percentage of the full marks
did D get?
a) 33%
b) 56%
c) 66-%
d) 75%
e) 100%​

Answer 1

Answer:

33%

Step-by-step explanation:

Marks of D=marks of reference(A)/(1+%)(s)

Marks of D = 960/(1+0.25)(1+0.20)(1-0.20)

Marks of D = 800

% marks = (1200-800)/1200 * 100% ≈ 33%

If you're unable to get this, read below.

Let D scored 'x'.

C scored = 20% less than x

C scored = x - 20% of x = x - (20/100)x

C scored = x - 0.2x = 0.8x

Similarly,

B scored = 20% more than C

B scored = 20% more than 0.8x

B scored = 0.8x + (20/100)(0.8x) = 0.96x

Thus,

A scored = 25% more than 0.96x

A scored = 0.96x + (25/100)(0.96x)

A scored = 1.2x

As given, A scored 960, it means,

=> 1.2x = 960

=> x = 960/1.2 = 800

Therefore,

% marks of D = (total - got)/total x 100%

% marks of D = (1200 - 800)/1200 x 100%

% marks of D = 33.33% ≈ 33%

Answer 2

Answer:

Given :-

• An examination was conducted for 1200 marks.
• A scored 25% more than B and B secured 20% more than C.
• C scored 20% less than D.
• If A secured 960 marks.

To Find :-

• What is the percentage of the full marks does D get.

Solution :-

Let,

$\mapsto$ Total percentage of the full marks get by D be x

First, we have to find how much mark C gets :

$\dashrightarrow$ C scored 20% less than D :

$\implies \sf C\: scored =\: x - 20\% \times x$

$\implies \sf C\: scored =\: x - \dfrac{20}{100} \times x$

$\implies \sf C\: scored =\: x - \dfrac{20}{100}x$

$\implies \sf C\: scored =\: x - \dfrac{20x}{100}$

$\implies \sf C\: scored =\: \dfrac{100x - 20x}{100}$

$\implies \sf C\: scored =\: \dfrac{8\cancel{0}x}{10\cancel{0}}$

$\implies \sf C\: scored =\: \dfrac{8x}{10}$

$\implies \sf\bold{\purple{C\: scored =\: 0.8x}}$

Hence, the scored get by C is 0.8x .

Now, we have to find how much marks B gets :

$\dashrightarrow$ B secured 20% more than C :

• C scored = 0.8x

$\implies \sf B\: scored =\: 0.8x + 20\% \times 0.8x$

$\implies \sf B\: scored =\: 0.8x + \dfrac{20}{100} \times \dfrac{8x}{10}$

$\implies \sf B\: scored =\: 0.8x + \dfrac{160x}{1000}$

$\implies \sf B\: scored =\: \dfrac{8x}{10} + \dfrac{160x}{1000}$

$\implies \sf B\: scored =\: \dfrac{800x + 160x}{1000}$

$\implies \sf B\: scored =\: \dfrac{960x}{1000}$

$\implies \sf\bold{\pink{B\: scored =\: 0.96x}}$

Hence, the scored get by B is 0.96x .

Again, we have to find how much marks A gets :

$\dashrightarrow$ A scored 25% more than B :

• B scored = 0.96x

$\implies \sf A\: scored =\: 0.96x + 25\% \times 0.96x$

$\implies \sf A\: scored =\: 0.96x + \dfrac{25}{100} \times \dfrac{96x}{100}$

$\implies \sf A\: scored =\: 0.96x + \dfrac{2400x}{10000}$

$\implies \sf A\: scored =\: \dfrac{96x}{100} + \dfrac{2400x}{10000}$

$\implies \sf A\: scored =\: \dfrac{9600x + 2400x}{10000}$

$\implies \sf A\: scored =\: \dfrac{12x\cancel{000}}{10\cancel{000}}$

$\implies \sf A\: scored =\: \dfrac{12x}{10}$

$\implies \sf\bold{\green{A\: scored =\: 1.2x}}$

Hence, the scored get by A is 1.2 x .

Now, according to the question :

$\dashrightarrow$ A secured 960 marks :

$\implies \sf 1.2x =\: 960$

$\implies \sf \dfrac{12x}{10} =\: 960$

$\implies \sf 12x =\: 10 \times 960$

$\implies \sf 12x =\: 9600$

$\implies \sf x =\: \dfrac{\cancel{9600}}{\cancel{12}}$

$\implies \sf\bold{x =\: 800}$

Now, we have to find the percentage of the full marks get by D :-

$\implies \sf Marks\: percentage\: for\: D =\: \dfrac{1200 - 800}{1200} \times 100\%$

$\implies \sf Marks\: percentage\: for\: D =\: \dfrac{4\cancel{00}}{12\cancel{00}} \times \dfrac{\cancel{100}}{\cancel{100}}$

$\implies \sf Marks\: percentage\: for\: D =\: \dfrac{4}{12}$

$\implies \sf Marks\: percentage\: for\: D =\: 0.3333$

$\implies \sf\bold{\red{Marks\: percentage\: for\: D \approx 33\%}}$

$\therefore$ The percentage of the full marks get by D is 33%.

Hence, the correct options is option no (a) 33% .