Question

In 2015, ratio of the number of students taking examinations in x, y and z states are respectively 3 : 5 : 6. Next year, the number of students are increased by 20%, 10% and 20% respectively. If ratio of the number of students in states x and z becomes 1 : 2, then find the number of students who sit to take examination in 2015.
(a) 5000
(b) 6000
(c) 75000
(d) Data insufficient

Answer 1

Answer:

$\huge\boxed{\boxed{\texttt{OPTION D}}}$

Step-by-step explanation:

Ratio of students in x , y and z respectively is given as :-

3 : 5 : 6 .

Let the no of students be 3 x , 5 x and 6 x respectively .

Increased students :

3 x + 20% of 3 x

⇒ 3 x + 20/100 × 3 x

⇒ 3 x + 3 x / 5

⇒ ( 15 x + 3 x )/5

⇒ 18 x / 5

Similarly 5 x + 10% of 5 x

= 5 x + 10/100 × 5 x

= 5 x + 5 x / 10

= 5 x + x/2

= ( 10 x + x )/2

= 11 x/2

Again Increased students in z :

20% of 6 x + 6 x

= 6 x + 20/100 × 6 x

= 6 x + 6 x / 5

= ( 30 x + 6 x ) / 5

= 36 x / 5

Ratio of x : z = 1 : 2

= ( 18 x/5 ) : ( 36 x / 5 ) = 1 : 2

Hence data is insufficient because we cannot come to a conclusion with the given data .

We can only prove the given data .

However we cannot find the number of students .

Answer 2

$<b><i>$in 2015

let the number of students in x=3k

number of students in y=5k

number of students in z=6k

Next year, number of students in

x=3k+20 °\° of 3k =18k/5

number of students in y=5k+10 °/° of

5k=11k/2

number of students in z=6k+20 °/°

6k=36k/5

according to question

18k/5/36k/5 =1/2

thus data is insufficient