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In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option. Quantity A: 20% of students prefer to speak both English and Hindi while 40% of students prefer to speak Hindi and 55% of students prefer to speak English. 1300 students don’t prefer to speak both English and Hindi. Find the difference between the number of students who speak only English and only Hindi. Quantity B: 10 men can complete the work in 20 days while 30 women can complete the work in 40 days. If 8 men and 30 women started the work and they work for 8 days then left the work. The remaining work will be completed by a certain number of women in 57.6 days. Find the number of women who completed the remaining work.

In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option. Quantity A: 20% of students prefer to speak both English and Hindi while 40% of students prefer to speak Hindi and 55% of students prefer to speak English. 1300 students don’t prefer to speak both English and Hindi. Find the difference between the number of students who speak only English and only Hindi. Quantity B: 10 men can complete the work in 20 days while 30 women can complete the work in 40 days. If 8 men and 30 women started the work and they work for 8 days then left the work. The remaining work will be completed by a certain number of women in 57.6 days. Find the number of women who completed the remaining work. Correct Answer <span lang="EN-IN" style=" line-height: 107%; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial;">Quantity A &gt; Quantity B</span>

Quantity A:

Let the total number of students be N.

Number of students prefer to speak English = 55N / 100

Number of students prefer to speak Hindi = 40N / 100

Number of students who prefer to speak both Hindi and English = 20N / 100

Number of students who doesn’t speak Hindi and English = 1300

⇒ (55N / 100 – 20N / 100) + (40N / 100 – 20N / 100) + 20N / 100 + 1300 = N

⇒ 75N / 100 + 1300 = N

⇒ N = 5200

Number of students who speak only Hindi = 5200 × (40 / 100 – 20 / 100) = 1040

Number of students who speak only English = 5200 × (55 / 100 – 20 / 100) = 1820

⇒ Required difference = 1820 – 1040 = 780

Quantity B:

1 men 1 day's work = 1 / (10 × 20)

1 women 1 day's work = 1 / (30 × 40)

8 men and 30 women 1 day’s work = 8 / (10 × 20) + 30 / (30 × 40) = 13 / 200

⇒ 8 men and 30 women 8 days work = 104 / 200

⇒ Remaining work after 8 days = 1 – 104 / 200 = 96 / 200 = 12 / 25

Let number of women worked after 8 days be N.

N women 57.6 days Work = (N × 57.6) / (30 × 40) = 6N / 125

Then,

⇒ 6N / 125 = 12 / 25

⇒ N = 10

10 women completed the remaining work.

∴ Quantity A > Quantity B.

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