A transport company dispatches shipments using trucks that can carry loads in multiples of 8, 10, 12, 14, and 18 tons respectively. The manager wants to load each truck with slightly extra cargo — 3 tons more than a full multiple of these capacities — and still ensure uniformity. What is the smallest total load, greater than 1200 tons, that would leave a remainder of 3 tons when divided by any of these truck capacities?
(a) 1227
(b) 2243
(c) 2523
(d) 1303

Question

A transport company dispatches shipments using trucks that can carry loads in multiples of 8, 10, 12, 14, and 18 tons respectively. The manager wants to load each truck with slightly extra cargo &mdash; 3 tons more than a full multiple of these capacities &mdash; and still ensure uniformity. What is the smallest total load, greater than 1200 tons, that would leave a remainder of 3 tons when divided by any of these truck capacities?
(a) 1227
(b) 2243
(c) 2523
(d) 1303

ONLiNE UPSC · Accepted Answer

LCM of 8, 10, 12, 14, 18 = 2&sup3; &times; 3&sup2; &times; 5 &times; 7 = 2520
Smallest number > 1200 of form 2520k + 3:
Try k = 1 &rarr; 2520 &times; 1 + 3 = 2523
Hence, option c is correct.

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M Question 1	⏱ 0
A transport company dispatches shipments using trucks that can carry loads in multiples of 8, 10, 12, 14, and 18 tons respectively. The manager wants to load each truck with slightly extra cargo — 3 tons more than a full multiple of these capacities — and still ensure uniformity. What is the smallest total load, greater than 1200 tons, that would leave a remainder of 3 tons when divided by any of these truck capacities? (a) 1227 (b) 2243 (c) 2523 (d) 1303