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Question

Two brands of tyre X,Y were tested with following result. If combined mean is 31.7,
find a.

life(miles) XY
20−2510
25−302224
30−356476
35−40a0
40−4530

A
6
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B
10
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C
12
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D
4
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Solution

The correct option is B 10
Life(miles) Classmark
A
X Y AX AY
2025 22.5 1 0 22.5 0
2530 27.5 22 24 605 660
3035 32.5 64 76 2080 2470
3540 37.5 a 0 37.5a 0
4045 42.5 3 0 127.5 0
X=90+a Y=100 AX=2835+37.5a AY=3130
¯¯¯¯¯X=AXX=2835+37.5a90+a

¯¯¯¯Y=AYY=3130100=31.3

Combined mean =X.¯¯¯¯¯X+Y.¯¯¯¯YX+Y

31.7=(90+a).2835+37.5a90+a+100×31.390+a+100

31.7=2835+37.5a+3130190+a

31.7=5965+37.5a190+a

6023+31.7a=5965+37.5a
58=5.8a
a=10

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