Question

A year ago, the cost of maruti and figo were in the ratio of 3 : 4. The ratio of present and past year costs of maruti and figo are 5 : 4 and 3 : 2. If the sum of their present cost is 7.8 lacs then find the ratio of present cost?
$
  {\text{A}}{\text{.}}\dfrac{{\text{9}}}{{\text{8}}} \\
  {\text{B}}{\text{.}}\dfrac{{\text{3}}}{2} \\
  {\text{C}}{\text{.}}\dfrac{{\text{5}}}{{\text{8}}} \\
  {\text{D}}{\text{.}}\dfrac{{\text{9}}}{{\text{7}}} \\
$

Answer 1

Hint: In order to get this problem right we need assume the variable x and make the equations according to the problem by solving the ratio of a year ago and the present year then you will get the value of x and with the help of x you will get the present rate of maruti and figo. Doing this will solve your problem and will give you the right answer.

Complete step-by-step answer:
Let the cost of Figo a year ago F = x
A year ago, ration of Maruti and figo = 3:4
Cost of Maruti last year = M (given)
So, we can do,
M : F = 3:4
M = $\left( {\dfrac{3}{4}} \right)$ F
Therefore, M = 0.75x...............(1)
For Maruti, the ratio of present rate and the rate a year ago is given as 5:4.
So, we can do:
M present : M = 5:4
Present cost of Maruti M present = $\left( {\dfrac{5}{4}} \right)$M
On substituting from equation 1 we get,
M present = 1.25 × 0.75 x
M present = 0.9375x......(2)
For Figo,
F present: F = 3:2
Therefore we can also say that F present: = 1.5 x ... (3)
As given that sum of maruti and figo for present = 7.8
M present + F present = 7.8
Substituting values from equation2 and 3, we get
0.9375x + 1.5x = 7.8
2.4375x = 7.8
x = 7.8 ÷ 2.4375
x = 3.2
We got the value of x that is the present rate of the figo as 3.2 lacs.
Then the value of M present will be 1.5x = 1.5(3.2)=4.8
Then the ratio will be $\dfrac{{{\text{M present}}}}{{{\text{F present}}}} = \dfrac{{4.8}}{{3.2}} = \dfrac{3}{2}$.
Hence the ratio is 3:2.
So, the correct answer is 3:2.

Note: When you get to solve such a problem always try to get the value of variables by making the equations from the given information in the question. Then solving the problem to get what is asked you will get the right answer. Knowing this thing will help you solve such types of problems.