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Q.

The total of the daily wages of Ram, Shyam and Mohan is Rs. $450$ . If they respectively spend $25 %, 20 %$ and $50 %$ of their income then ratio of their savings become $9 : 8 : 4$ . What is the income of Ram?

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a

180

b

190

c

200

d

175

answer is A.

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Detailed Solution

For solving this question, we will first suppose the income of Ram, Shyam and Mohan as x, y and z respectively. Then we will find their spent income using the given percentage in the form of variables. Using them, we will find their savings in the form of variables. After that, we will compare the ratio of their savings with the given ratio and take a common value of all ratios as k. Using total wages, we will find the value of k and then values of x, y and z which are required income.
Incomes of mohan be x,y and z
So, x+y+z = 450……(i)
Ram spends 20% of the income
Savings of Ram=

x - \frac{25}{100} x = \frac{3 x}{4}

Savings of shyam=

y - \frac{20}{100} y = \frac{4 y}{5}

Savings of mohan=

z - \frac{50}{100} z = \frac{z}{2}

Ratio of the saving=

\frac{3 x}{4} : \frac{4 y}{5} : \frac{z}{2}

=9:8:4

\frac{3 x}{4} = 9 k; \frac{4 y}{5} = 8 k; \frac{z}{2} = 4 k

\Rightarrow x = 12 k; y = 10 k; z = 8 k

From (i)

x + y + z = 450

\Rightarrow 12 k + 10 k + 8 k = 450

\Rightarrow 30 k = 450

\Rightarrow k = 15

Income of ram is

x = 12 k = 12 \times 15 = 180

So, Income of ram Rs 180
Hence option 1 is correct.

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