SSC CGL Tier II 1 Dec 2016 Paper 1

Question : 48 of 100

Marks: +1, -0

If A borrowed Rs. P at x% and B borrowed Rs. Q (> P) at y% per annum at simple interest at the same time, then the amount of their debts will be equal after

100 $( { {Q}- {P}}/{ {Px}- {Q} y} )$ years
100 $( { {Px}- {Q} y}/{ {Q}- {P}} )$ years
100 $( { {Px}- {Q} y}/{ {P}- {Q}} )$ years
100 $( { {P}- {Q}}/{ {Px}- {Q} y} )$ years

Validate

Solution:

(1) Let amounts be equal in T years.
S.L.

= { { \Principal } × { \Time } ×{ \Rate }}/{100}

∴{P}+ { {P}×{x}×{T}}/{100}

= {Q}+ { {Q} ×{y} ×{T}}/{100}

⇒{ {P}×{T}}/{100}- { {Q} {y} {T}}/{100}= {Q}- {P}

⇒T ( { {Px}- {Q} {y}}/{100} )= {Q}- {P}

⇒T= 100 ( { {Q}- {P}}/{ {Px}- {Q} y} )

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