Mathematics
A man saved ₹ 33,000 in 10 months. In each month after the first, he saves ₹ 100 more than he did in the preceding month. How much did he save in the first month?
AP
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Answer
Let the man saved ₹ a in first month.
The amount the man saved each month forms an Arithmetic Progression (A.P.) where :
Total sum saved Sn = ₹ 33,000.
Number of months (n) = 10
He saves ₹ 100 more than he did in the preceding month.
Thus, d = 100
We know that,
Sum of n terms of an A.P. is given by,
∴ Sn = [2a + (n - 1)d]
⇒ 33000 = [2a + (10 - 1)100]
⇒ 33000 = 5[2a + (9)100]
⇒ = [2a + 900]
⇒ 6600 = [2a + 900]
⇒ 6600 - 900 = 2a
⇒ 2a = 5700
⇒ a =
⇒ a = ₹ 2,850.
Hence, the amount man saved in first month is ₹ 2,850.
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