Directions (Q. No. 19 – 20) : Answer the following questions based on the information and diagram given below :
An automobile company has advertised for the appointment of trainee engineers in different disciplines. First the applications received are thoroughly scrutinized and good ones are called to the main centre of the company for two written tests and a viva. The written tests are of 2 hrs duration each.

The first written test E₁ checks the general scientific background and the second written test E₂ checks the basics of the discipline. Earlier all the candidates were required to appear in both E₁ and E₂ but only those who clear both were allowed to appear in the viva for final selection.
To minimize the cost, the company has decided to change the procedure. Now they want to conduct this exam in three stages.
In the first stage they may offer the candidate to sit in either written test (E₁ or E₂) and if s/he passes in that he/she will go for next stage in which company may take his/her other written test or viva. If he passes in this second stage, he will go for the remaining exam in third stage.
A candidate has to pass both the exams and viva for final selection. A candidate is rejected if s/he fails at any stage. The expenses are ₹ 500 per candidate for conducting each of E₁, E₂ or Viva (V). The following historical data for 100 candidates is available from previous selections.

19. What is the ratio of the “percentage of candidates clearing E₂ exam in second stage after clearing E₁ exam in first stage” to “percentage of candidates clearing E₁ exam in second stage after clearing E₂ exam in first stage” ?

20. What is the percentage of candidates who are failing in second stage viva exam after clearing E₂ exam in first stage ?

Directions (Q. No. 21 – 22) : These questions are based on the information and diagram given below :
A survey was conducted on a sample of 500 cinema artists with reference to their proficiency in the skill of acting, singing and dancing. The results of the survey are depicted in the given Venn diagram.

21. What is the ratio of the number of cinema artists who are not proficient in any of these three skills (X₀) to those who are proficient in all three (X₃)?

22. If all other data remains same, how many cinema artists who are not proficient in any of these three skills should become proficient in all three, so that the above said ratio between number of cine-artists who are not proficient in any of these three skills (X₀) to those who are proficient in all three (X₃) should now become X₀ : X₃ = 1 : 4 ?

10. At a party there are 3 large pizzas of equal size. Each pizza has been cut into 9 equal pieces. \(8 \over9\) of the first pizza has been eaten; \(2 \over3\)of the second pizza has been eaten; \(7 \over9\)of the third pizza has been eaten. What fraction of the 3 pizzas is left ?