Question

A man started saving money from the first week of January 2017. He saved 525 in the first week, 340
in the second week, 55 in the third week and so on, till the last week of December 2017. Find the total
saving of the man in the year 2017.

​

Answer 1

SOLUTION

GIVEN

A man started saving money from the first week of January 2017. He saved ₹ 25 in the first week, ₹ 40 in the second week, ₹ 55 in the third week and so on, till the last week of December 2017.

TO DETERMINE

The total saving of the man in the year 2017.

EVALUATION

Here it is given that a man started saving money from the first week of January 2017.

He saved ₹ 25 in the first week, ₹ 40 in the second week, ₹ 55 in the third week and so on, till the last week of December 2017

So the savings are 25 , 40 , 55 ,....

So the terms are in Arithmetic Progression

First term = a = 25

Common Difference = d = 40 - 25 = 15

There are 52 weeks in the year 2017

So n = 52

Hence total saving of the man in the year 2017.

$\displaystyle \sf{ = \frac{n}{2} \bigg[ 2a + (n - 1)d\bigg] }$

$\displaystyle \sf{ = \frac{52}{2} \bigg[ 2 \times 25 + (52- 1) \times 15\bigg] }$

$\displaystyle \sf{ = 26 \times \bigg[ 50+ (51 \times 15) \bigg] }$

$\displaystyle \sf{ = 26 \times \bigg[ 50+ 765\bigg] }$

$\displaystyle \sf{ = 26 \times 815 }$

$\displaystyle \sf{ =21190 }$

FINAL ANSWER

The total saving of the man in the year 2017 = ₹ 21190

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