Total runs scored by three batsmen x, y and z are 1584. The ratio of runs scored by x апау is 4 : 3 and y and z is 5 : 3. How many runs are scored by x?

Total runs scored by three batsmen x, y and z are 1584. The ratio of runs scored by x апау is 4 : 3 and y and z is 5 : 3. How many runs are scored by x?

(SSC MTS 21 Sep 2017 Shift 1)

(A) 742 (B) 614

(C) 516 (D) 720

Let’s denote the runs scored by x, y, and z as \(X\), \(Y\), and \(Z\) respectively. The given information can be expressed in the form of equations:

1. \(X + Y + Z = 1584\) (The total runs scored by three batsmen)
2. The ratio of runs scored by x and y is 4:3, so \(X:Y = 4:3\).
3. The ratio of runs scored by y and z is 5:3, so \(Y:Z = 5:3\).

Now, let’s use these ratios to express \(Y\) and \(Z\) in terms of \(X\):

\[Y = \frac{3}{4}X\]
\[Z = \frac{3}{5}Y\]

Now, substitute these expressions into the total runs equation:

\[X + \frac{3}{4}X + \frac{3}{5} \times \frac{3}{4}X = 1584\]

Combine the terms with common denominators:

\[\frac{20}{20}X + \frac{15}{20}X + \frac{9}{20}X = 1584\]

Combine the numerators:

\[\frac{44}{20}X = 1584\]

Divide by the common factor (20):

\[2.2X = 1584\]

Now, solve for \(X\):

\[X = \frac{1584}{2.2}\]

\[X = 720\]

Therefore, \(x\) scored 720 runs.

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