A can do a certain work in 12 days and B can do the same work in 18 days. They worked together for 3 days. The remaining work was completed by B and C working, together, in 3 1/2 days. C alone will complete
33 1/3% of the whole work in
Answers
Answer:
Answer:
\text{10th term}10th term = \sf\red{-1}−1
\huge\bf\underline\mathfrak{Step \: by \: step \: explanation :}
Stepbystepexplanation:
\huge\bf\underline\mathfrak{Given :}
Given:
\text{3rd term + 8th term of the A.P. = 7}3rd term + 8th term of the A.P. = 7
\text{7th term + 14th term = -3}7th term + 14th term = -3
\huge\bf\underline\mathfrak{To \: find :}
Tofind:
\text{10th term of the A.P.}10th term of the A.P.
\huge\bf\underline\mathfrak{Solution :}
Solution:
\sf\underbrace{General \: term \: of \: an \: A.P. \: :-}
GeneraltermofanA.P.:−
⠀⠀⠀⠀⠀⠀⠀⠀⠀\sf a_n=a \: + \: ( \: n - 1 \: )da
n
=a+(n−1)d
Where,
a = \text{First term}First term
d = \text{Common difference}Common difference
\underline\text{From the above formula, we can say :-}
From the above formula, we can say :-
⠀⠀⠀⠀⠀⠀⠀⠀⠀\text{3rd term}3rd term = \sf\purple{a+2d}a+2d
⠀⠀⠀⠀⠀⠀⠀⠀⠀\text{8th term}8th term = \sf\purple{a+7d}a+7d
⠀⠀⠀⠀⠀⠀⠀⠀⠀\text{7th term}7th term = \sf\purple{a+6d}a+6d
⠀⠀⠀⠀⠀⠀⠀⠀⠀\text{14th term}14th term = \sf\purple{a+13d}a+13d
\sf\underbrace{According \: to \: question \: :-}
Accordingtoquestion:−
⠀⠀⠀⠀⠀⠀⠀⠀⠀\color{green}\star\:\tt{Case \: 1 \: :-}⋆Case1:−
\sf{a_3+a_8 = 7}a
3
+a
8
=7
\implies⟹ \sf{a + 2d + a + 7d = 8 }a+2d+a+7d=8
\implies⟹ \sf{2a + 9d = 8}2a+9d=8 --- \text{Equation (i)}Equation (i)
⠀⠀⠀⠀⠀⠀⠀⠀⠀\color{green}\star\:\tt{Case \: 2 \: :-}⋆Case2:−
\sf{7th \: term + 14th \: term}7thterm+14thterm = -3
\implies⟹ \sf{a + 6d + a + 13d = -3 }a+6d+a+13d=−3
\implies⟹ \sf{2a + 19d = -3}2a+19d=−3 --- \text{Equation (ii)}Equation (ii)
\sf\underbrace{Solving \: both \: equations \: :-}
Solvingbothequations:−
⠀⠀⠀⠀⠀⠀⠀⠀⠀\sf\red{a = 8}a=8 and \sf\red{d = -1}d=−1
\sf\underbrace{Finding \: 10th \: term \: :-}
Finding10thterm:−
\sf{10th \: term = a + 9d }10thterm=a+9d
\implies⟹ \sf{8 + 9(-1)}8+9(−1)
\implies⟹ \sf\purple{-1}−1
Step-by-step explanation:
c can alone complete remain work in 23 days