SSC CHSL Model Paper 14

Question : 59 of 100

Marks: +1, -0

Divide Rs. 25300 into 3 parts so that their amounts in 4, 6 and 8 years respectively may be equal, the rate of interest being 5% per annum at simple interest. What is the first part?

Rs. 1110
Rs. 17500
Rs. 8400
Rs. 9100

Validate

Solution:

Let the parts be x, y and 25300 (x + y).
So,

x+{x×4×5}/100=y+{y×6×5}/100

=z +{z×8×5}/100

⇒

x+x/5=y+{3y}/10=z+{2z}/5

⇒

{6x}/5={13y}/10={7z}/5

⇒

{12x}/10={13y}/10={14z}/10=k

(let’s say)
Therefore ,

x={10k}/12,y={10k}/13

and

z={10k}/14

Now,

x + y + z = 2 5 3 0 0

⇒

{10k}/12+{10k}/13+{10k}/14=25300

LCM of 12, 13, 14 is 1092
⇒

{91 + 1 0k + 84 + 1 0k + 78 + 10k}/1092

=25300

⇒

10k (91 + 8 4 + 78) = 2 5 3 0 0× 1092

⇒

k={2 5 3 0 ×1 0 9 2}/253

⇒

k = 1 09 20

Therefore,

x={10k}/12=109200/12=9100

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