Question

A physical quantity Q depends upon three quantities x, y and zas
x2y12
In a particular set of measurements, x is
measured with +50% error, y is measured with –36% error and z is measured with -20% error. The percentage error in the
calculation of Q in this set of measurements is 251%. Find the value of n.
Z
Answer:
ОО
o 1
02
3
4
05
O 6
07
8
09
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Answer 1

Explanation:

Step-by-step explanation:

Find LCM of 15, 20, 36, and 48

\begin{gathered}\begin{array}{r|l} 2 & 15,20,36,48 \\\cline{1-2} 3 & 15,10,18,24 \\\cline{1-2} 5 & 5,10,6,8 \\\cline{1-2} 2 & 1,2,6,8\\\cline{1-2} 3 & 1,1,3,4\\\cline{1-2}2&1,1,1,4 \\\cline{1-2}2&1,1,1,2 \\\cline{1-2} & 1,1,1,1 \end{array}\end{gathered}

2

\cline1−23

\cline1−25

\cline1−22

\cline1−23

\cline1−22

\cline1−22

\cline1−2

15,20,36,48

15,10,18,24

5,10,6,8

1,2,6,8

1,1,3,4

1,1,1,4

1,1,1,2

1,1,1,1

(If you're an app user refer the attachment)

LCM = 2 × 3 × 5 × 2 × 3 × 2 × 2

\longrightarrow⟶ 6 × 10 × 6 × 2

\longrightarrow⟶ 60 × 12

\longrightarrow⟶ 720

Least common multiple of 15, 20, 36, and 48 is 720.

Add 3 to their LCM

\longrightarrow⟶ 720 + 3

\longrightarrow⟶ 723

Therefore, 723 is the least number which when divided separately by 15, 20, 36, and 48 leaves 3 as remainder in each case.

___________________

Verification:

723 ÷ 15

\longrightarrow⟶ Quotient = 48

\longrightarrow⟶ Remainder = 3

723 ÷ 20

\longrightarrow⟶ Quotient = 36

\longrightarrow⟶ Remainder = 3

732 ÷ 36

\longrightarrow⟶ Quotient = 20

\longrightarrow⟶ Remainder = 3

732 ÷ 48

\longrightarrow⟶ Quotient = 15

\longrightarrow⟶ Remainder = 3