Question

X, Y and Z invest in the ratio of 3 : 5 : 7. The percentages of return on their investments are in the ratio of 5 : 4 : 5. Find the total earnings, if Y earns Rs. 450 more than X (in Rs.).
Select one:
a. 5200
b. 6300
c. 5600 .
d. 4500 .​

Answer 1

Hint: As you observe in the question, the investments of X,Y and Z are given as a ratio. Also the percentage of return on their investments is given in ratio form. We have to consider the percentage return of each on their investment separately. The earning can be calculated by finding out the return after their investment. We can use the relation between X and Y’s earnings given in the question, which is earning of X + Rs 450 = Earning of B.

Complete step by step solution:For X:

5% return is obtained on investment of 3x. Thus earning is 5/100×3X

or 0.05×3X

For Y:

4% return is obtained on investment of 5x. Thus earning is 4/100×5X

or 0.04×5X

Now the relation between X and Y's earnings is given as:

Earnings of X + 250 = Earning of Y

⇒5/100×3x+450=4/100×5x

⇒(15X−20X)/100=−450

⇒−5X/100=−450

(the negative sign on both sides get cancelled)

⇒5X=450×100

⇒x=450×100/2

=Rs9000

Therefore the value x is Rs 9000

Thus earning of X is 5/100×3X

=5/100×3×9000=Rs1350

Earning of Y is 4/100×5X

=4/100×5×9000=Rs1800

Earning of Z 5/100×7X

=5/100×7×9000=Rs3150

Total earnings = 1350+1800+3150

=Rs 6300

Answer 2

Given:

The investment ratio of X, Y, and Z is 3:5:7. The returns of their investments are in the ratio 5:4:5. The final earning of Y is Rs 450 more than the final earnings of X.

To Find:

The combined final earnings of X, Y, and Z together are?

Solution:

1. Let the investments of X, Y, and Z be 3i, 5i, and 7i.

2. Let the returns of X, Y, and Z be 5r, 4r, and 5r respectively.

3. 5r% of return is obtained on investment of 3i for X,

=> Earning of X = (5r x 3i)/100 = 15ri/100.

=> 4r% of return is obtained on investment 5i of  for Y,

=> Earning of Y = (4rx5i)/100 = 20ri/100.

=> 5r% of return is obtained on investment 7i of  for Z,

=> Earning of Y = (5rx7i)/100 = 35ri/100.

4. Y earns Rs 450 more than X,

=> 20ri/100 = 450 + 15ri/100,

=> 20ri/100 -15ri/100 = 450,

=> (20ri-15ri)/100 = 450,

=> 5ri/100 = 450,

=> 5ri = 45000,

=> ri = 9000.

5. The earnings of X, Y, and Z are,

=> earnings of X = 15(9000)/100 = Rs 1350,

=> earnings of Y = 20(9000)/100 = Rs 1800,

=> earnings of  Z = 35(9000)/100 = Rs 3150.

=> Total earnings of X, Y, and Z is 1350 + 1800 + 3150 = Rs 6300.

Hence, the total earnings of X, Y, and Z is Rs 6300. Option B is the correct answer.