A lift has the capacity of 18 adults or 30 children. How many children can board the lift with 12 adults?

(a) 6
(b) 10 ✓ UPSC's answer
(c) 12
(d) 15

Why the answer is (b)

• The lift's capacity is defined as 18 adults or 30 children, establishing a ratio where 18 adults are equivalent to 30 children in weight or space.

• Simplifying this ratio, 1 adult is equivalent to 30/18 = 5/3 children.

• If 12 adults board the lift, their combined capacity usage is 12 * (5/3) = 20 children's worth of capacity.

• The total capacity of the lift is 30 children.

• The remaining capacity for children is 30 - 20 = 10 children.

• Therefore, 10 children can board the lift with 12 adults, which corresponds to option (b).

Why the other options are wrong

(a) 6: Option (a) is incorrect because 6 children would only account for 26 units of capacity (12 adults + 6 children equivalent), leaving 4 units unused.
(c) 12: Option (c) is incorrect because 12 children would require 24 units of capacity, which combined with 12 adults (20 units) exceeds the total capacity of 30 units.
(d) 15: Option (d) is incorrect because 15 children would require 25 units of capacity, which combined with 12 adults (20 units) significantly exceeds the total capacity of 30 units.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2018, held on 3 June 2018. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.