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 full capacity is stated as 18 adults or 30 children, meaning the total weight of 18 adults equals the total weight of 30 children.
• From this, the weight of one adult equals 30/18 = 5/3 children.
• Twelve adults therefore occupy a weight equivalent to 12 × (5/3) = 60/3 = 20 children.
• The lift's total capacity in child-equivalents is 30, so the remaining capacity after 12 adults board is 30 − 20 = 10 children.
• Hence, 10 children can board the lift alongside the 12 adults, which corresponds to option (b).
Why the other options are wrong
- (a) 6
- Six children would correspond to a remaining capacity of only 6 child-equivalents, implying the 12 adults occupy 24 child-equivalents, which would require 1 adult = 2 children — inconsistent with the given ratio of 1 adult = 5/3 children.
- (c) 12
- Twelve children would leave a remaining capacity of 12 child-equivalents, implying the 12 adults occupy only 18 child-equivalents, i.e., 1 adult = 1.5 children, which contradicts the correct ratio of 5/3 children per adult.
- (d) 15
- Fifteen children would leave a remaining capacity of 15 child-equivalents, implying the 12 adults occupy only 15 child-equivalents, i.e., 1 adult = 1.25 children, which does not match the 5/3 ratio derived from the 18-adult / 30-child capacity.
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.