Direction: The following question are accompanied by two statements (...
From statement I:
Let the efficiency of each boy be 3a unit/day.
Then, the efficiency of each girl = 4a unit/day.
According to question,
10 × x × 3a = 15 × y × 4a
⇒ 30x = 60y
⇒ x : y = 2 : 1
Also, x + y = 18
So, x =
23 × 18 = 12
⇒ y = 18 – 12 = 6
Let the number of days taken by (x – 4) boys and (y – 3) girls together to complete the same work be ‘D’ days.
Then,
[(12 – 4) × 3a + (6 – 3) × 4a] × D = 15 × 6 × 4a
⇒ (24a + 12a) × D = 360a
⇒ D = 360a ÷ 36a
⇒ D = 10 days
Statement I alone is sufficient to answer the question.
Statement II:
Since x = 2y
Now the number of days taken by all the girls is half the number of days taken by all the boys.
Then the efficiency of girls is twice the efficiency of boys.
Let the efficiency of each boy be a unit/day.
Then, the efficiency of each girl = 2a unit/day.
According to question,
10 × x × a = 15 × y × 2a
⇒ 10x = 15y
⇒ x : y = 3 : 2
Statement II alone is not sufficient to answer the question.
Hence, the correct option is (A).