# 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.