# TCS Papers: Sample Questions 5 - 7 of 502

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## Question number: 5

### Write in Short

Find the value of M (363,5) + R (3.4) + T (7.8) – R (3.8) where M is modulus, R is round-off, T is truncate.

### Explanation

• M denotes modulus operation, R denotes round-off and T denotes truncation operation.
• M (363,5): Dividing 363 by 5, remainder will be 3.
• R (3.4): As 0.4 is less than 0.5, it will be rounded off to 3.
• T (7.8): Removing fractional part, 7.8 will be truncated to 7.
• R (3.8): As 0.8 is greater than 0.5, it will be rounded off to 4.
• Given expression will be reduced to
• So, value of the given expression will be 9.

## Question number: 6

### Write in Short

Calculate the value of the 678 to the base 7.

### Explanation

• Here, the given number 678 is in decimal number.
• We are asked to find its base 7 number.
• To convert any decimal number into base – N number, we need to follow this procedure.
• Dividing 678 by 7, quotient will be 96 and remainder will be 6
• Dividing 96 by 7, quotient will be 13 and remainder will be 5
• Dividing 13 by 7, quotient will be 1 and remainder will be 6
• Dividing 1 by 7, quotient will be 0 and remainder will be 1
• Reversing the order of remainders, we can get the base 7 equivalent number of decimal number 678.
• Base 7 number of 678 is 1656

## Question number: 7

### Write in Short

Ten years ago X was half of Y. If the ratio of their present ages is , what will be the total of their present ages?

### Explanation

• Let the present age of X is x years and Y is y years.
• Before 10 years, X was half of Y, i. e.

• Ratio of their present ages is , i. e.

• Solving both the equations,

x = 15 and y = 20

• We are asked to find the total of their present ages.
• It will be,
• Total of present ages of X and Y is 35 years.