Mani saves money in a jar at home for six months.

Question

Mani saves money in a jar at home for six months. The first month he saves S dollars. Each month thereafter, Mani saves 1/2 of what he has saved the previous month. If Mani’s total savings at the end of the six months is $393.75, how much money does he save the sixth month?

(A) $6.25
(B) $7.50
(C) $12.50
(D) $18.75
(E) $25.00

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paragw · Answer

Mani saves money as follows for 6 months:
S, S/2, S/4, S/8, S/16, S/32
This is GP and Sn for this GP = S /(1/2-1)
Also we've to find  money he save in the sixth month i.e. S/32 
On simplifying, we get 63S/32 = 393.75
S/32 = 6.25
Hence,  A

Dereno · Answer

Let the money saved by Mani on The first day be S

Second day, it’s S/2

Third day , (S/2)/2 = S/4

Fourth day, (S/4)/2 = S/8

Fifth day , (S/8)/2 = S/16

Sixth day, (S/16)/2 = S/32

S + (S/2) + (S/4) + (S/8) + (S/16) + (S/32) = $ 393.25

LCM as 32, we get (32S + 16 S + 8S + 4S+ 2S+ S)/32 = $393.25

63 S = $393.25*32

S = approx 200

we need S/32 = 200/32 =  $ 6.25

Option A

S1mple3 · Answer

Sixth month saving be S.

TOTAL savings = S+2S+4S+8S+16S+32S = 63S = 393.75 $, 
 S= 6.25$, A

Souradeep17 · Answer

So if i consider that it is 32S in 1st month then it will 16s in 2nd month, 8s in 3rd month. 4S in 4th month and 2S in 5th month and S in 6th

Sum of them 63S=393.75
S=393.75/63=6.25 (option A)

Reon · Answer

Mani saves money in a jar at home for six months. The first month he saves S dollars. Each month thereafter, Mani saves 1/2 of what he has saved the previous month. If Mani’s total savings at the end of the six months is $393.75, how much money does he save the sixth month?

First Month= S
Second month= S/2 
Third month = S/4 .....
Sixth month= S/32 
Sum of savings in 6 months= S+(S/2)+(S/4)+(S/8)+(S/16)+(S/32) = (32S+16S+8S+4S+2S+S)/32 = 63S/32 
63S/32 = 393.75 
S=393.75*32/63 = 200 
Savings in 6th month = S/32 =200/32= 6.25

A

CareerLauncherIE · Answer

Here is the solution of the question:-

We know Mani saves  $S = first month  and each month thereafter he saves half of the previous month. The total savings after 6 months is $393.75.
Instead of summing as a series, notice that  each month is half of the previous :
 
 Month 6 = 1/32 of Month 1 
 Month 5 = 1/16 of Month 1 
 Month 4 = 1/8 of Month 1 
 Month 3 = 1/4 of Month 1 
 Month 2 = 1/2 of Month 1 
 Month 1 = S  
The total savings = Month1 + Month2 + ... + Month6 = $393.75

Now, factor S:

S×(1+1/2+1/4+1/8+1/16+1/32)=393.75
S * 63/32 = 393.75
S = 393.75 * (32)/(63) = 200

Since Month 6 = S/32:

Month 6 savings=200/32=6.25

Final Answer:  Option(A). $6.25

Mani saves money in a jar at home for six months.

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Mani saves money in a jar at home for six months.

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