G.C.E.O-Level Maths Problem

题目

G.C.E.O-Level Maths Problem
This is one of the question from the papaer in 1984
One hundred office workers use various combinations of travel by bus,train and car to reach their offices.of these one hundred workers,42 use buses,43 use cars and 66 use trains; 18 use both bus and train but not car,and 23 use train and car but not bus.There are no workers who use bus and car but not train.Every worker uses at least one of bus,train and car/
Denoting by x the number of workers who use all three means of transport.And Calculate x

答案

X=10 10 WORKERS USE THREE MEANS OF TRANSPORT
SINCE BUS: 42 PPL BUS & TRAIN: 18 PPL
THEREFORE, PEOPLE ONLY USE BUS=42-18=24 PPL
SINCE CAR: 43 PPL TRAIN & CAR: 23 PPL
THEREFORE, PEOPLE ONLY USE CAR: 43-23=20 PPL
SINCE TRAIN: 66
THEREFORE, PEOPLE ONLY USE TRAIN: 66-18-23=25 PPL
BUS & CAR: 0 TOTAL WORKERS: 100
24+18+23+20+25=110 -> 110-100=10 PPL
IN SUMMARY:
ONLY BUS: 24
ONLY CAR: 20
ONLY TRAIN: 25
ONLY BUS & TRAIN: 8
ONLY CAR & TRAIN: 13
BUS, CAR & TRAIN: 10