Question

In a sports complex, the strength of athletes is 29%, 400 are footballers and the rest are cricketers. Ratio of the cricketers, footballers and athletes is 9 ∶ 8 ∶ 7. If some new athletes join the complex then . Find the correct statements.

a) The number of new athletes join the complex to make the percentage of athletes  40% are 600.

b) Total number of players in the complex are 1500.

Choose the correct answer from the given option(s).

1. Only a
2. Only b
3. Both a and b
4. Neither a nor b

Answer 1

Correct Answer - Option 4 : Neither a nor b

Given∶

29% of the total players are athletes. 

400 are footballers.

Given Ratio of the cricketers, footballers and athletes = 9 ∶ 8 ∶ 7.

Formula Used∶

Basics of percentage and ratio.

Cancelled out HCF reintroduction technique.

Calculation∶

Using basic ratio concepts and cancelled out HCF reintroduction technique, The actual number of cricketers, footballers and athletes.

May be assumed as 9x, 8x and 7x respectively with x as the cancelled out HCF.

As number of Football players are 200, we get the value of x easily as

8x = 400

x = 400/8

⇒ 50

So, total number of players = 9x + 8x + 7x = 24x

⇒ 24x = 24 

× 50

⇒ 1200

Total players = 1200

So, statement a is wrong.

Number of Athletes,

⇒ 

7x = 7 × 50 = 350

Assume that number of new athletes as y.

So, 0.5(1200 + y) = 350 + y

⇒ 600 + 0.5y = 350 + y

⇒ 0.5y = 600 - 350

⇒0.5y - 250

⇒ y = 500

500 new athletes join the complex to make the percentage of athletes as 50%.

So, statement b is also wrong.

∴ The correct option is 4 (neither a nor b)