CAT 2018 Question Paper Shift 2 Solved Paper

Question : 84 of 100

Marks: +1, -0

Gopal borrows Rs. X from Ankit at 8% annual interest. He then adds Rs. Yof his own money and lends Rs. X+Y to Ishan at 10% annual interest. At theend of the year, after returning Ankit’s dues, the net interest retained byGopal is the same as that accrued to Ankit. On the other hand, had Gopallent Rs. X+2Y to Ishan at 10%, then the net interest retained by him wouldhave increased by Rs. 150. If all interests are compounded annually, thenfind the value of X + Y.

Your Answer:

Validate

Solution:

Interest to be repaid to Ankit at the end of the year

=0.08 {X}

Interest that Gopal would receive from Ishan in two cases are as given.
Case I: if he lends

{X}+ {Y}

Interest received

=(X+Y) × 0.1=0.1 X+0.1 Y

Interest retained by Gopal after paying to Ankit

=(0.1 {X}+0.1 {Y})-(0.08 {X})=0.02 {X}+0.1 {Y}

Given that Interest retained by Gopal is same as that accrued by Ankit

⇒(0.02 {X}+0.1 {Y})=0.08 {X}

⇒ Y=0.6 {X}

Case II: if he lends

{X}+2 Y

Interest received

=( {X}+2 {Y}) × 0.1=0.1 {X}+0.2 {Y}

Interest retained by Gopal after paying to Ankit

=(0.1 {X}+0.2 {Y})-(0.08 {X})=0.02 {X}+0.2 {Y}

Given that interest retained by Gopal would increase by 150

⇒(0.02 {X}+0.2 {Y})-(0.02 {X}+0.1 {Y})=150

0.1 {Y}=150

⇒ {Y}=1500

and

{X}=1500 × 0.6=2500

Hence

{X}+ {Y}=2500+1500=4000

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