GATE Mechanical 2019 Set 1 | GA | Question: 7

Question

A person divided an amount of Rs. $100,000$ into two parts and invested in two different schemes. In one he got $10 \%$ profit and in the other he got $12 \%$. If the profit percentages are interchanged with these investments he would have got Rs. $120$ less. Find the ratio between his investments in the two schemes.

• A. $9:16$
• B. $11:14$
• C. $37:63$
• D. $47:53$

Answer 1

Let $X$ be his investment in the first scheme and $Y$ be in the second scheme.

We have,

$1.1X + 1.12 Y = 1.12X + 1.1 Y+120$

$\implies 0.02Y = 0.02X + 120$

$\implies 2Y = 2X + 12000$

$\implies Y = X +6000$

Since $X + Y = 100,000, 2X  = 94,000 \implies X = 47,000$

$\implies Y = 47,000 + 6000 = 53,000$

So, $X : Y = 47:53.$

Correct Option: D.

Comments

In one he got 10% profit and in the other he got 12%. If the profit percentages are interchanged with these investments he would have got Rs. 120 less.

I think they were talking about profit and not about the total returns (investment + returns) itself.

so, the equation should be:

$0.10X + 0.12Y = 0.12X + 0.10Y + 120$

but because this difference (120) is in profits and in both equations we are including profits while rest everything (investment, ratio or relation b/w investments) is unchanged so both these equations work fine.

Answer 2

$\dfrac{SP_{1}-x}{x}\times 100=10\ \ \ ..........(1)$

$\dfrac{SP_{2}-(100,000-x)}{100,000-x}\times 100=12\ \ \ ..........(2)$

$SP_{1}=\dfrac{110x}{100}$          $SP_{2}=\dfrac{11200000-112x}{100}$

$SP_{1}+SP_{2}=\dfrac{11200000-2x}{100}$

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$\dfrac{SP_{1new}-x}{x}\times 100=12\ \ \ ..........(3)$

$\dfrac{SP_{2new}-(100,000-x)}{100,000-x}\times 100=10\ \ \ ..........(4)$

$SP_{1new}=\dfrac{112x}{100}$          $SP_{2new}=\dfrac{11000000-110x}{100}$

$SP_{1new}+SP_{2new}=\dfrac{11200000+2x}{100}$

---

$SP_{1}+SP_{2}-SP_{1new}+SP_{2new}=120$

 

$\dfrac{11200000-2x}{100}-\dfrac{11200000+2x}{100}=120$

$200000-4x=12000$

$x=47,000$

$100,000-x=53,000$

 

$Ratio= 47:53$

Answer 3

let the two amounts in the schemes be x,100000-x

10/100x,12/100(100000-x) are profits

when we interchange the amounts the values are

10/100(100000-x),12/100(x)

we can write 10/100*(100000-x)+12/100*(x)+120=10/100*(x)+12/100*(100000-x) (loss 120)

we will get x=470000,100000-x=530000

so the ratio is 47/53

Answer 4

ans.

Answer 5

 

The correct option is C 47 : 53
First condition

Total amount = 100000

Assume, A has invested Rs. x at 10% rate and Rs (100000 - x) at 12% interest.

Total interest = 0.1x + (100000 - x) × 0.12
(Tl)I=12000−0.02x

Second condition

Assume, A has invested Rs x at 12% rate and Rs (100000 - x) at 10% interest.

Total interest = 0.12x + (100000 - x) × 0.1
(Tl)II=10000+0.02x

Given,
(Tl)I−(Tl)II=120

(12000 - 0.02x) - (10000 + 0.02x) = 120
2000 - 0.04x = 120

x=18800.04=Rs. 47000

Now, Another part
= 100000 - x
= 100000 - 47000
= Rs. 53000
x(100000−x)=4753

Answer 6

X+Y=1,00,000--------1

X*1.1+Y*1.12=(X*1.12+Y*1.1)+120------ 2

0.02X-0.02Y=  -120----2

MULTIPLY 100 WITH EQUATION 2

X-Y= -6000

ADD EQ[1+2]

X=47,000

Y=53,000

47 : 53 IS ANSWER

OPTION D-> 47:53