வெல்லுங்கள் CSAT 2025 - 14: Q and A - Problems on age and boat

Questions & Answers (Multiple Choice) - Problems on age and boat
கொள்குறி வினா- விடைகள் - வயது & படகு கணக்குகள்

1. A is 12 years younger than B. After four years ,B will be twice as old. Find the present age of A.
a. 20 b. 8 c. 12 d. 24

2. A is 5 times as old as B. If sum their ages is 72. Find the difference of their ages.
a. 24 b. 32 c. 48 d. 60

3. Six years ago Ram is twice as old as Ravi. After 9 years twice Ram's age is three times Ravi’s age. Find the sum of their present ages.
a. 45 b. 60 c. 54 d. 57

4. The present ages of A and B are in the ratio 4 : 5 and after five years they will be in the ratio of 5 : 6. Find the sum of their ages five years ago.
a. 35 b. 45 c. 55 d. 65

5. A man is 25 years older than his son. After 5 years, he will be twice as old his son. What was the age of his son five years ago?
a. 40 b. 25 c. 15 d. 20

6. The sum of the ages four children born at the intervals of 3 years each is 54 years. What is the age of the eldest child?
a. 20 b. 21 c. 16 d. 18

7. The average of 9 directors in a company as it was three years ago, a younger man having been substituted for one of the directors. How many years younger was the new director than the director he took place?
a. 25 b. 27 c. 36 d. 18

8. A says yo B, 'I am twice as old as you were when I was as you were'. The sum of their ages is 65. Find the age of A.
a. 39 b. 26 c. 36 d. 24

9. The speed of the boat in still water is 15kmph. A man sailed through the boat 60km down stream in three hours. What is the speed of the stream?
a. 3 kmph b. 2.5kmph
c. 5 kmph d. 4 kmph

10. A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat (in still water) and the stream is
a. 1 : 3 b. 2 : 3
c. 3 : 2 d. 3 : 1

11. A man can row three-quarters of a kilometre against the stream in 10 minutes and down the stream in 6 minutes. The speed (in km/hr) of the man in still water is:
a. 3 kmph b. 6 kmph
c. 5 kmph d. 8 kmph

12. A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes him 50 minutes to row to a place and come back, how far is the place?
a. 2 km b. 3 km
c. 4 km d. 6 km

13. A boat takes 45 minutes less to travel 18 km downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 kmph, the speed of the stream is
a. 1 kmph b. 1.5 kmph
c. 2 kmph d. 3 kmph

14. A motorboat, whose speed in 10 km/hr in still water goes 20 km downstream and comes back in a total of 4 hours 10 minutes. The speed of the stream (in km/hr) is
a. 3 kmph b. 1.5 kmph
c. 1 kmph d. 2 kmph

15. A man can row 40k against the stream in 5 hours and 70km down the stream in 7hours. The speed (in km/hr) of the man in still water is
a. 10 kmph b. 9 kmph
c. 12 kmph d. 8 kmph

Answers

1. b 2. c 3. d 4. a 5. c

6. d 7. b 8. a 9. c 10. d

11. b 12. a 13. c 14. d 15. b

Explanation to answers

1. Let the present ages of A and be 'a'
and 'b' respectively.
After four years 'a+4' and 'b+4'
By problem
a = b - 12 ; b + 4 = 2(a + 4)
=> b + 4 = 2(b - 12 + 4)
=> b = 20, a = 20 - 12 = 8

2. Let the present ages of A and B be 'a'
and 'b' respectively.
By problem
a = 5b ; a + b = 72
= > 6b = 72 => b = 12
Difference of their ages
a - b = 5b - b = 4b = 48.

3. Six years ago let the ages of Ram and Ravi be '2a' and 'a' respectively.
By problem
Present ages are '2a + 6' and 'a + 6'
After 9 years, '2a + 15' and 'a + 15'
Here 2(2a + 15) = 3(a + 15)
=> a = 15
Sum of their present ages
= 2a + 6 + a + 6 = 3a + 12 = 57

4. Let the present ages of A and B be '4a'
and '5a' respectively.
By problem
After 5 years the ages of A and B will be '4a+5' and '5a+5'
But 4a+5 : 5a+5 = 5 : 6
=> 6(4a+5) = 5(5a+5)
=> a = 5
Present ages are 20 and 25
Their ages five years ago, 15 and 20.
Sum of their ages five years ago is 35.

5. Let 's' be the present age of the son.
So father's age is 's + 25'.
After 5 years, son's age will be 's+5'
Father's age will be 's+30'.
But s + 30 = 2(s+5)
=> s = 20
5 years ago son's age was 15 years.

6. Let the present ages of four children be c, c + 3, c + 6, c + 9.
So, 4c + 18 = 54 => 4c = 36
=> c = 9
Hence the age of the eldest child is
c + 9 = 18 years.

7. Total age of all 9 directors must be 27 years (3×9) greater than what it was three years ago. Given that no change in the average age of all.
Hence the new director is 27 years younger than the old director who left.

8. Let the present ages of A and B be 'a'
and 'b' respectively.
By problem
(a - b) years ago, A's age was
a - (a - b) = b
But (a - b) years ago, B's age was
b - (a - b) = 2b - a.
By problem b = 2(2b - a)
=> 3b = 2a => b = (2/3)a
But a + b = 65 => a + (2/3)a = 65
=> a = 65 × 3/5 = 39.

9. If x kmph is the speed of thr boat in still water and current or water speed is
y kmph, then the downstream and upstream are 'x+y' and 'x-y' respectively.
Here x = 15 ; x+y = 60/3 = 20.
So the speed of the stream is
(20 - 15) = 5 kmph.

10. If x kmph is the speed of thr boat in still water and current or water speed is
y kmph, then the downstream and upstream are 'x+y' and 'x-y' respectively.
Here d/(x - y) = 2{d/(x+y)}
=> x + y = 2x - 2y
=> 3y = x => x/y = 3/1
So x : y = 3 : 1

11. Here (x - y) ×(10/60) = 3/4
=> (x - y) = 45/10 = 4.5
And (x + y) ×(6/60) = 3/4
=> (x + y) = 15/2 = 7.5
So 2x = 4.5 + 7.5 =12
=> x = 6.

12. Let d be the distance
So d/6 + d/4 = 50/60
=> (5d)/(12) = 5/6 => d = 2 km
Another method
d = [{(us)×(ds)}/{(us)+(ds)}] × t
Here us = 5 - 1 = 4 ds = 5 + 1 = 6
t = 50/60 hrs.
So d = {(6×4)/(6+4)} × (50/60) = 2 km.

13. Let 'y' kmph be the speed of the stream.
Here {18/(10-y)} - {18/(10+y)} = 45/60
=> {1/(10-y)} - {1/(10+y)} = 1/24
=> 10+y - 10+y = (1/24) (100 - y^2)
=> y^2 + 48y -100 = 0
=> (y - 2) (y + 50) = 0
=> y = 2 or y = -50
Since y cannot be negative, y = 2 kmph.

14. Let 'y' kmph be the speed of the stream.
Here {20/(10-y)} +{20/(10+y)} = 250/60
=> {1/(10-y)} + {1/(10+y)} = 5/24
=> 10+y +10-y = (5/24) (100 - y^2)
=> 5y^2 -500+480 = 0
=> 5y^2 = 20
=> y = 2 or y = - 2
Since y cannot be negative, y = 2 kmph.

15. If x kmph is the speed of the boat in still water and current or water speed is
y kmph, then the downstream and upstream are 'x+y' and 'x-y' respectively.
x + y = 70/7 = 10
x - y = 40/5 = 8
=> 2x = 18 => x = 9.
So the speed of the boat in still water is
9kmph.

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