averages Model Questions & Answers, Practice Test for ssc mts paper 1
The sum of the ages of a mother and her daughter is 50 yrs. Also 5 yrs ago, the mother’s age was 7 times the age of the daughter. What are the present ages of the mother and the daughter?
Answer: (a)
Let the age of the daughter be x yrs.
Then, the age of the mother is (50 – x) yrs.
5 yrs ago, 7(x – 5) = 50 – x – 5
or, 8x = 50 – 5 + 35 = 80
∴ x = 10
Therefore, daughter's age = 10 yrs
and mother's age = 40 yrs
The ratio between the present ages of P and Q is 3 : 4 respectively. Four years hence Q will be 5 years older than P. What is P’s present age?
Answer: (b)
Let the present ages of P and Q be 3x and 4x respectively.
After 4 years
4x – 3x = 5
∴ x = 5
∴ P's present age = 3x
= 3 × 5 = 15 years
10 Yrs ago, Sita’s mother was 4 times older than her daughter. After 10 yrs, the mother will be two times older than the daughter. What is the present age of Sita?
Answer: (c)
Shortcut method :
Daughter's age = ${10(4 - 1) + 10(2 - 1)}/{4 - 2}$ = 20 yrs
The average of 50 consecutive natural numbers is x. What will be the new average when the next four natural numbers are also included ?
Answer: (a)
Sum of n consecutive natural numbers = n (n + 1)/2
Average of n consecutive natural numbers
= (n + 1)/2
For first 50 average = 51/2 = x
When next 4 natural numbers are included.
Then, average of 54 continues natural number = $55/2$
= $51/2 + 4/2 = x + 2$
The total marks obtained by a student in physics, Chemistry and Mathematics together is 120 more than the marks obtained by him in Chemistry. What are the average marks obtained by him in Physics and Mathematics together ?
Answer: (b)
Suppose marks got in physics, chemistry and mathematics are P, C and M.
P + C + M = C + 120
∴ P + M = 120
$\text"P + M"/2$ = 60
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