5 + Interview Questions in MIX in MISCELLANEOUS Page 1 InterviewSolution

1.	Direction: In a college, there are total 280 students. The ratio of boys and girls is 4 : 3. In a college fest, they perform in 3 events viz. Singing, Dancing and Drama. In singing event, 50% of the total girls and 40% of the total boys perform. In dancing event, 30% of the total girls and 30% of the total boys perform. In drama event, 20% of the total girls and 30% of the total boys perform. 12 boys and 15 girls are performing in both singing and dancing. 10 boys and 13 girls are performing in both dancing and drama. 9 boys and 14 girls are performing in both drama and singing. 4 boys and 5 girls are performing in all three events. (Some of the students are not performing in any event)What is the ratio of boys and girls performing in singing event only?1). 47 : 362). 37 : 263). 33 : 264). 27 : 17
Answer»

Discussion

2.	In an annual function, 504 children participated. The ratio of the number of girls to the number of boys is 5 : 3 respectively. Out of the total girls, 20% participated in dance and remaining girls participated in solo song, group song and drama in the ratio of 2 : 3 : 4. Two – third of the total boys participated in group song and the remaining boys participated in solo song and dance in the ratio of 4:5What is the approximate percentage of the boys who have participated in dance out of the total number of boys?1). 19%2). 23%3). 16%4). 27%
Answer» Given that total number of students are 504 in which GIRLS to boys ratio is 5 : 3. Let the total number of girls be X then total number of boys will be (504 - X). $(\therefore \frac{X}{{504 - X}} = \frac{5}{3})$ 3X = 2520 – 5X ⇒ 8X = 2520 ⇒ Total number of girls, X = 315 And, total number of boys = 504 – 315 = 189 Now, given that 2/3^rd of boys participated in group song. Hence 1/3^rd of boys participated in solo song and dance in the ratio of 4:5. ⇒ One-third of total boys = 1/3 × 189 = 63 Let the number of boys participated in dance be D then, ∴ Number of boys participated in solo song = 63 – D Hence, $(\frac{{63 - D}}{D} = \frac{4}{5}\;)$ ⇒ 315 – 5D = 4D ⇒ 9D = 315 Hence, Number of boys participated in dance, D = 35 ∴ Required percentage = 35/189 × 100 = 18.518% ~ 19 %

2.

In an annual function, 504 children participated. The ratio of the number of girls to the number of boys is 5 : 3 respectively. Out of the total girls, 20% participated in dance and remaining girls participated in solo song, group song and drama in the ratio of 2 : 3 : 4. Two – third of the total boys participated in group song and the remaining boys participated in solo song and dance in the ratio of 4:5What is the approximate percentage of the boys who have participated in dance out of the total number of boys?1). 19%2). 23%3). 16%4). 27%

Answer»

Given that total number of students are 504 in which GIRLS to boys ratio is 5 : 3.

Let the total number of girls be X then total number of boys will be (504 - X).

$(\therefore \frac{X}{{504 - X}} = \frac{5}{3})$

3X = 2520 – 5X

⇒ 8X = 2520

⇒ Total number of girls, X = 315

And, total number of boys = 504 – 315

= 189

Now, given that 2/3^rd of boys participated in group song.

Hence 1/3^rd of boys participated in solo song and dance in the ratio of 4:5.

⇒ One-third of total boys = 1/3 × 189

= 63

Let the number of boys participated in dance be D then,

∴ Number of boys participated in solo song = 63 – D

Hence, $(\frac{{63 - D}}{D} = \frac{4}{5}\;)$

⇒ 315 – 5D = 4D

⇒ 9D = 315

Hence, Number of boys participated in dance, D = 35

∴ Required percentage = 35/189 × 100

= 18.518%

~ 19 %

Discussion

3.	30% of the number of passengers of train B is in sleeper class coaches. 10% of the total passengers of train B are in first class coaches.What is sum of the total number of passengers in the general coaches of train A and the AC coaches of train B together?1). 4492). 4593). 4354). 445
Answer» Number of passengers in train A = 700 ? Train B has 30% more passengers than train A, Number of passenger in train B = 700 + 30% of 700 = 910 ? In train A, 20% of the passengers are in general CONCHES, Number of passengers in the general coaches of train A = 20% of 700 = 140 According to the information given in the problem, one-fourth (i.e. 25%) of the total number of passengers in train A are in AC coaches and total number ofpassengers in AC coaches in both the trains together is 480. ∴ Number of passengers in the AC coaches of train B = 480 – (25% of 700) = 480 – 175 = 305 ∴ Total number of passengers in the general coaches of train A and AC coaches of train B together = 140 + 305 =445

3.

30% of the number of passengers of train B is in sleeper class coaches. 10% of the total passengers of train B are in first class coaches.What is sum of the total number of passengers in the general coaches of train A and the AC coaches of train B together?1). 4492). 4593). 4354). 445

Answer»

Number of passengers in train A = 700

? Train B has 30% more passengers than train A,

Number of passenger in train B = 700 + 30% of 700 = 910

? In train A, 20% of the passengers are in general CONCHES,

Number of passengers in the general coaches of train A = 20% of 700 = 140

According to the information given in the problem, one-fourth (i.e. 25%) of the total number of passengers in train A are in AC coaches and total number ofpassengers in AC coaches in both the trains together is 480.

∴ Number of passengers in the AC coaches of train B = 480 – (25% of 700) = 480 – 175 = 305

∴ Total number of passengers in the general coaches of train A and AC coaches of train B together = 140 + 305 =445

Discussion

4.	Not surprisingly the growth of the hotel industry is driven by the increase in the number of people using hotel and the increase in per person use of the hotel.In 2004, it was expected that there will be 200 million hotel users in India or about 20% of the population will generate Rs. 50 billion in hotel revenues. Industry revenues should expand from Rs. 50 billion to Rs. 150 billion by 2008, while the number of users should grow to over 560 million or to about half the population of India in the same period.What was the percentage growth in the number of hotel users over the given period?1). 45%2). 100%3). 180%4). 90%
Answer» According to the INFORMATION given in the problem, Number of hotel users in India in 2004 = 200 million Number of hotel users in India in 2008 = 560 million ∴ % GROWTH in the number of users over the given period $(= \FRAC{{560 - 200}}{{200}} \times 100)$ $(= \;\frac{{360}}{{200}} \times 100 = 180{\rm{\;}})$

4.

Not surprisingly the growth of the hotel industry is driven by the increase in the number of people using hotel and the increase in per person use of the hotel.In 2004, it was expected that there will be 200 million hotel users in India or about 20% of the population will generate Rs. 50 billion in hotel revenues. Industry revenues should expand from Rs. 50 billion to Rs. 150 billion by 2008, while the number of users should grow to over 560 million or to about half the population of India in the same period.What was the percentage growth in the number of hotel users over the given period?1). 45%2). 100%3). 180%4). 90%

Answer»

According to the INFORMATION given in the problem,

Number of hotel users in India in 2004 = 200 million

Number of hotel users in India in 2008 = 560 million

∴ % GROWTH in the number of users over the given period $(= \FRAC{{560 - 200}}{{200}} \times 100)$

$(= \;\frac{{360}}{{200}} \times 100 = 180{\rm{\;}})$

Discussion

5.	In an annual function, 504 children participated. The ratio of the number of girls to the number of boys is 5 : 3 respectively. Out of the total girls, 20% participated in dance and remaining girls participated in solo song, group song and drama in the ratio of 2 : 3 : 4. Two – third of the total boys participated in group song and the remaining boys participated in solo song and dance in the ratio of 4:5What is the total number of girls who have participated in group song and drama together?1). 1922). 1953). 1844). 168
Answer» Given that 80% of girls participated in solo, group SONG and drama in ratio 2 : 3 : 4. ⇒ 80% of total girls = 80/100 × 315 = 252 ∴ Number of girls participated in group song and drama $(= \frac{{3 + 4}}{{2 + 3 + 4}} \TIMES 252)$ = 196

5.

In an annual function, 504 children participated. The ratio of the number of girls to the number of boys is 5 : 3 respectively. Out of the total girls, 20% participated in dance and remaining girls participated in solo song, group song and drama in the ratio of 2 : 3 : 4. Two – third of the total boys participated in group song and the remaining boys participated in solo song and dance in the ratio of 4:5What is the total number of girls who have participated in group song and drama together?1). 1922). 1953). 1844). 168

Answer»

Given that 80% of girls participated in solo, group SONG and drama in ratio 2 : 3 : 4.

⇒ 80% of total girls = 80/100 × 315

= 252

∴ Number of girls participated in group song and drama $(= \frac{{3 + 4}}{{2 + 3 + 4}} \TIMES 252)$

= 196

Discussion

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30% of the number of passengers of train B is in sleeper class coaches. 10% of the total passengers of train B are in first class coaches.What is sum of the total number of passengers in the general coaches of train A and the AC coaches of train B together?1). 4492). 4593). 4354). 445