Advertisements
Advertisements
Question
If twice the son’s age in years is added to the mother’s age, the sum is 70 years. But, if twice the mother’s age is added to the son’s age, the sum is 95 years. Find the age of the mother and that of the son.
Solution
Let the mother’s present age be x years.
Let her son’s present age be y years.
Then, we have:
x + 2y = 70 …….(i)
And, 2x + y = 95 ……(ii)
On multiplying (ii) by 2, we get:
4x + 2y = 190 ……..(iii)
On subtracting (i) from (iii), we get:
3x = 120
⇒ x = 40
On substituting x = 40 in (i), we get:
40 + 2y = 70
⇒ 2y = (70 – 40) = 30
⇒ y = 15
Hence, the mother’s present age is 40 years and her son’s present age is 15 years.
APPEARS IN
RELATED QUESTIONS
Draw the graph of the equation y – x = 2
Find the value of k for which each of the following system of equations has infinitely many solutions :
2x + (k - 2)y = k
6x + (2k - 1)y - (2k + 5)
Find the value of k for which each of the following system of equations have no solution
kx - 5y = 2
6x + 2y = 7
For what value of , the following system of equations will be inconsistent?
4x + 6y - 11 = 0
2x + ky - 7 = 0
Find the values of a and b for which the system of linear equations has an infinite number of solutions:
(2a – 1) x + 3y = 5, 3x + (b – 1)y = 2.
Find the values of k for which the system of equations 3x + ky = 0,
2x – y = 0 has a unique solution.
If 12x + 17y = 53 and 17x + 12y = 63 then find the value of ( x + y)
Solve for x:
3x2-2x-83=0
Find the value(s) of p in (i) to (iv) and p and q in (v) for the following pair of equations:
2x + 3y = 7 and 2px + py = 28 – qy,
if the pair of equations have infinitely many solutions.
Read the following passage:
|
A coaching institute of Mathematics conducts classes in two batches I and II and fees for rich and poor children are different. In batch I, there are 20 poor and 5 rich children, whereas in batch II, there are 5 poor and 25 rich children. The total monthly collection of fees from batch I is ₹9,000 and from batch II is ₹26,000. Assume that each poor child pays ₹x per month and each rich child pays ₹y per month.
|
Based on the above information, answer the following questions:
- Represent the information given above in terms of x and y.
- Find the monthly fee paid by a poor child.
OR
Find the difference in the monthly fee paid by a poor child and a rich child. - If there are 10 poor and 20 rich children in batch II, what is the total monthly collection of fees from batch II?
