CASELET-1 [SBI PO 21/06/2014]

Directions (Q. No. 1-7): Study the following information carefully to answer the questions.

               

In a medical college there are 1600 students studying Dentistry and Homeopathy. Each student from each course knows one or more languages out of English, Hindi and Bengali. 45% of the students study Dentistry and the remaining students study Homeopathy.

                Out of the students studying Dentistry, boys and girls are in the ratio of 5:3

                Out of the boys studying Dentistry, 16% know only English, 10% know only Hindi and 4% know only Bengali. 24% know English as well as Hindi, 20% know English as well as Bengali and 14% know Hindi as well as Bengali. The remaining boys know all the three languages.

                Out of the girls studying Dentistry, 20% know only English, 10% know only Hindi and 10% know only Bengali. 20% know English as well as Hindi, 20% know English as well as Bengali and 10% know Hindi as well as Bengali. The remaining girls know all the three languages.

                Out of the students studying Homeopathy, boys and girls are in the ratio of 4:7.

                Out of the boys studying Homeopathy, 20% know only English, 15% know only Hindi and 5% know only Bengali. 15% know English as well as Hindi, 25% know English as well as Bengali, and 10% know Hindi as well as Bengali. The remaining boys know all three languages.

                Out of the girls studying Homeopathy, 15% know only English, 15% know only Hindi and 5% know only Bengali. 20% know English as well as Hindi, 20% know English as well as Bengali, and 15% know Hindi as well as Bengali. The remaining girls know all three languages.

1. How many students studying Dentistry know only either English or Hindi? [Ans. (4) 198]

(1) 166   (2) 162   (3) 308   (4) 198   (5) 248

2. How many students in the college know all three languages? [Ans. (3) 169]

(1) 108   (2) 132   (3) 169   (4) 137   (5) 142

3. What percent of the total no. of girls in the college know Bengali? [Ans. (5) 50]

(1) 45   (2) 40   (3) 48   (4) 42   (5) 50

4. How many students studying Homeopathy do not know English? [Ans. (1) 292]

(1) 292   (2) 232   (3) 228   (4) 298   (5) 207

5. Out of the students studying Homeopathy, what is the ratio of the no. of boys knowing English to the no. of girls knowing Hindi? [Ans. (2) 2:3]

(1) 3:5   (2) 2:3   (3) 9:11   (4) 9:13   (5) 1:3

6. Out of the total no. of students studying Dentistry, what percent knows at least two languages? [Ans. (4) 66 & 1/4]

(1) 61 & 12/13   (2) 57 & 13/16   (3) 59 & 13/17   (4) 66 & 1/4   (5) 62 & 12/19

7. What percent of the total no. of girls in the college do not know Hindi? (Rounded off to nearest integer)  [Ans. (5) 43]

(1) 38   (2) 46   (3) 48   (4) 36   (5) 43

Solution:

Detailed Explanation: Total no. of students in the medical college is 1600. They study Dentistry and Homeopathy. Each student from each course knows one or more languages out of English, Hindi and Bengali. 45% of the students study Dentistry and the remaining students study Homeopathy.

No. of students studying Dentistry = 45% of 1600 = 720

No. of students studying Homeopathy = 55% of 1600 = 880

                Given that, out of the students studying Dentistry, boys and girls are in the ratio of 5:3

So, no. of boys studying Dentistry = 5/8 of 720 = 450

And, no. of girls studying Dentistry = 3/8 of 720 = 270

It is also given that out of the students studying Homeopathy, boys and girls are in the ratio of 4:7.

So, no. of boys studying Homeopathy = 4/11 of 880 = 320

And, no. of girls studying Homeopathy = 7/11 of 880 = 560

1. How many students studying Dentistry know only either English or Hindi? [Ans. (4) 198]

(1) 166   (2) 162   (3) 308   (4) 198   (5) 248

Solution: 16%+10% = 26% of boys and 20%+10% = 30% of girls are studying only either English or Hindi.

26% of 450 = 117

30% of 270 = 81

Therefore, total no. of students (studying Dentistry know only either English or Hindi) = 117+81 = 198 Ans.

2. How many students in the college know all three languages? [Ans. (3) 169]

(1) 108   (2) 132   (3) 169   (4) 137   (5) 142

Solution: 12% of 450+10% of 270+10% of 320+10% of 560 = 54+27+32+56 = 169 Ans.

3. What percent of the total no. of girls in the college know Bengali? [Ans. (5) 50]

(1) 45   (2) 40   (3) 48   (4) 42   (5) 50

Solution: [20%+10%+10%+10% =] 50% of 270 + [20%+10%+5%+15% =] 50% of 560 = 135+280 = 415 Ans.

4. How many students studying Homeopathy do not know English? [Ans. (1) 292]

(1) 292   (2) 232   (3) 228   (4) 298   (5) 207

Solution: [5%+10%+15% =] 30% of 320 + [5%+15%+15% =] 35% of 560 = 96+196 = 292 Ans.

5. Out of the students studying Homeopathy, what is the ratio of the no. of boys knowing English to the no. of girls knowing Hindi? [Ans. (2) 2:3]

(1) 3:5   (2) 2:3   (3) 9:11   (4) 9:13   (5) 1:3

Solution: [20%+10%+15%+25% =] 70% of 320 : [20%+10%+15%+15% =] 60% of 560  = 7×32 : 6×56 = 2 : 3 Ans.

6. Out of the total no. of students studying Dentistry, what percent knows at least two languages? [Ans. (4) 66 & 1/4]

(1) 61 & 12/13   (2) 57 & 13/16   (3) 59 & 13/17   (4) 66 & 1/4   (5) 62 & 12/19

Solution: [24%+14%+12%+20% =] 70% of 450 + [20%+20%+10%+10% =] 60% of 270 = 315+162 = 477

Required percentage = (477/720) × 100 = (66 & ¼)% Ans.

7. What percent of the total no. of girls in the college do not know Hindi? (Rounded off to nearest integer)  [Ans. (5) 43]

(1) 38   (2) 46   (3) 48   (4) 36   (5) 43

Solution: [20%+20%+10% =] 50% of 270 + [15%+20%+5% =] 40% of 560 = 135+224 = 359

Required percentage = (359/830) × 100 = 43.25% ≡ 43% approx. Ans.

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