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CAT 2001 — QA Question 45

Simple EquationsEasy
Passage / Data

Answer the following question based on the information given below.

The batting average (BA) of a test batsman is computed from runs scored and innings played-completed innings and incomplete innings (not out) in the following manner:

r1 = number of runs scored in completed innings; n1 = number of completed innings

r2 = number of runs scored in incomplete innings; n2 = number of incomplete innings

BA = r1+r2n1

To better assess batsman's accomplishments, the ICC is considering two other measures MBA1 and MBA2 defined as follows:

MBA1 = r1n1+n2n1× max[0, (r2n2-r1n1])

MBA2 = r1+r2n1+n2

A change making machine contains 1 rupee, 2 rupee and 5 rupee coins. The total number of coins is 300. The amount is Rs. 960. If the number of 1 rupee coins and the number of 2 rupee coins are interchanged, the value comes down by Rs. 40. The total number of 5 rupee coins is

Answer & solution

  • A

    100

  • 140

  • C

    60

  • D

    150

Solution

Let the number of Re. 1, Re. 2 and Re. 5 coins be x, y and z respectively.

x + y + z = 300                           ...(i)

x + 2y + 5z = 960                       ...(ii)

2x + y + 5z = 920                       ...(iii)

Adding equation (ii) and equation (iii), we get,

3x + 3y + 10z = 1880                 ...(iv)

Multiply equation (i) by 3, we get,

3x + 3y + 3z = 900                     ...(v)

Subtracting equation (v) from equation (iv), we get,

7z = 980

∴ z = 140

Hence, option (b).

CAT 2001 QA Q45: A change making machine contains 1 rupee, 2 rupee and 5 rupee coins. The total number of coins is 300. The amo — Solution | TheCATExam