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Sequences and Series Ncert Solutions Maths class 11th Maths Class 11th Sequence and Series

106. 150 workers were engaged to finish a job in a certain number of days. 4 workers dropped out on second day, 4 more workers dropped out on third day and so on. It took 8 more days to finish the work. Find the number of days in which the work was completed.

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Payal Gupta | Contributor-Level 10

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106. Let ‘x’ be the no of days in which 150 workers took to finish the job.

If 150 workers worked for x days then number of workers for x days =150 x.

But given that number of works dropped 4 on 2^nd day, then 4 on 3^rd day and so on taking 8 more

days to finish the work. i.e., x + 8 days we can express as.

150 x = 150 + (150 $-$ 4) + (150 $-$ 4 $-$ 4)+……+ (x + 8) days.

150 x = 150 + 146 + 142 +……… (x+8) days which

R.H.S. from as A.P. of

a = 150

d = -4 and n = x +8

So, S_n = 150 x

$\Rightarrow \frac{n}{2} [2 \times 150 + (n - 1) (- 4)] = 150 x$

n [ 150 + (n - 1) (-2)] = 150 (n - 8) [ $?$ n = x +8 x $-$ 8 $-$ x]

150n 2n (n - 1

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106. Let ‘x’ be the no of days in which 150 workers took to finish the job.

If 150 workers worked for x days then number of workers for x days =150 x.

But given that number of works dropped 4 on 2^nd day, then 4 on 3^rd day and so on taking 8 more

days to finish the work. i.e., x + 8 days we can express as.

150 x = 150 + (150 $-$ 4) + (150 $-$ 4 $-$ 4)+……+ (x + 8) days.

150 x = 150 + 146 + 142 +……… (x+8) days which

R.H.S. from as A.P. of

a = 150

d = -4 and n = x +8

So, S_n = 150 x

$\Rightarrow \frac{n}{2} [2 \times 150 + (n - 1) (- 4)] = 150 x$

n [ 150 + (n - 1) (-2)] = 150 (n - 8) [ $?$ n = x +8 x $-$ 8 $-$ x]

150n 2n (n - 1) 150n 1200

2n² + 2n 1200 =0

n² - n - 600 = 0 [ dividing by -2 throughout]

n² - 25 n + 24 n 600 = 0

n (n - 25) + 24 (n - 25) = 0

(n - 25) (n + 24) = 0

n = 25 or n = -24 (which is not possible)

So, n = 25 days

i.e. x + 8 = 25 days

less

106. Let ‘x’ be the no of days in which 150 workers took to finish the job.If 150 workers worked for x days then number of workers for x days =150 x.But given that number of works dropped 4 on 2nd day, then 4 on 3rd day and so on taking 8 moredays to finish the work. i.e., x + 8 days we can express as.150 x = 150 + (150 <math><mrow><mo>−</mo></mrow></math> 4) + (150 <math><mrow><mo>−</mo></mrow></math> 4 <math><mrow><mo>−</mo></mrow></math> 4)+……+ (x + 8) days.150 x = 150 + 146 + 142 +……… (x+8) days whichR.H.S. from as A.P. ofa = 150d = -4 and n = x +8So, Sn = 150 x<math><mrow><mo>⇒</mo><mfrac><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo stretchy="false"> [</mo><mn>2</mn><mo>×</mo><mn>1</mn><mn>5</mn><mn>0</mn><mo>+</mo><mo stretchy="false"> (</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo stretchy="false">)</mo><mo stretchy="false"> (</mo><mo>−</mo><mn>4</mn><mo stretchy="false">)</mo><mo stretchy="false">]</mo><mo>=</mo><mn>1</mn><mn>5</mn><mn>0</mn><mi>x</mi></mrow></math>n [ 150 + (n - 1) (-2)] = 150 (n - 8) [ <math><mrow><mo>? </mo></mrow></math> n = x +8 x <math><mrow><mo>−</mo></mrow></math> 8 <math><mrow><mo>−</mo></mrow></math> x]150n 2n (n - 1) 150n 12002n2 + 2n 1200 =0n2 - n - 600 = 0 [ dividing by -2 throughout]n2 - 25 n + 24 n 600 = 0n (n - 25) + 24 (n - 25) = 0 (n - 25) (n + 24) = 0n = 25 or n = -24 (which is not possible)So, n = 25 daysi.e. x + 8 = 25 days

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106. 150 workers were engaged to finish a job in a certain number of days. 4 workers dropped out on second day, 4 more workers dropped out on third day and so on. It took 8 more days to finish the work. Find the number of days in which the work was completed.

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