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Arithmetic : Level 3 Test -8

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Question 1
I have one-rupee coins, 50-paisa coins and 25-paisa coins. The number of coins are in the ratio 2.5 : 3 : 4. If the total amount with me is Rs. 210, find the number of one-rupee coins
Question 1 Explanation: 
The number of coins are in the ratio 2.5 : 3 : 4.,
Therefore the values will be (1 × 2.5) : (0.5 × 3) : (0.25 × 4) = 2.5 : 1.5 : 1 or 5 : 3 : 2
Therefore the total value = Rs. 210,
Let us assume the value of each coin 5r, 3r and 2r,
Therefore r = 210/10
So the total value of one-rupee coins will be 5 x (210/10) = Rs. 105
So the total number of one-rupee coins will be 105.
Question 2
A man travels from A to B at a speed h km/hr. He then rests at B for h hours. He then travels from B to C at a speed 2h km/hr and rests for 2h hours. He moves further to D at a speed twice as that between B and C. He thus reaches D in 16 hr. If distances A-B, B-C and C-D are all equal to 12 km, the time for which he rested at B could be:
3 hr
6 hr
2 hr
4 hr
Question 2 Explanation: 
Total time taken by the man to travel from A to D = 16 hr
Total distance travelled = 36 km.
The time taken by him without taking rest
= (16 – h – 2h) = (16 – 3h).
Now the time that he take to travel individual segments
12/h + 12/2h + 12/4h = 21/h ,
Therefore,21/h = (16 - 3h)
3h2 – 16h + 21 = 0.
Solving this equation,
we get h = 3 or h = 7/3
This should be the time for which he rested at B.
Question 3
A man travels three-fifths of a distance AB at a speed 3a, and the remaining at a speed 2b. If he goes from B to A and return at a speed 5c in the same time, then
1/a +1/b = 1/c
a + b = c
1/a +1/b = 2/c
none of these
Question 3 Explanation: 
Let the total distance be d.
Therefore the distance travelled by the man = 3d/5
Let the speed of man = 3a.
Therefore total time taken = 3d/15a = d/5a
Time = Distance/speed
Again distance traveled = 2d/5
Let speed = 2b.
Therefore, time taken = 2d/10b = d/5b
Total time take from A to B = d/15a + d/15b
Now he travels from B to A and comes back.
So total distance travelled = 2d
Let average speed = 5c.
Therefore time taken = 2d/ (5c),
Since the time taken in both the cases is same, we can write d/5a + d/5b = 2d/5c
Hence, 1/a + 1/b = 2/c
Question 4
In a mile race, Akshay can be given a start of 128 m by Bhairav. If Bhairav can give Chinmay a start of 4 m in a 100 m dash, then who out of Akshay and Chinmay will win a race of one and half miles, and what will be the final lead given by the winner to the loser? (One mile is 1,600 m.)
Akshay,1/2 mile
Chinmay, 1/32 mile
Akshay, 1/24 mile
Chinmay, 1/16 mile
Question 4 Explanation: 
Akshay can be given a start of 128 m by Bhairav.
Therefore akshay can cover 128 m and still complete one mile with him
Akshay can travel (1600 – 128) = 1,472 m.
Therefore the ratio of the speeds of Bhairav and Akshay = Ratio of the distances travelled by them in the same time
= 1600 / 1472 = 25 : 23.
Again Bhairav can give Chinmay a start of 4 miles.
Therefore if Bhairav runs 100 m, Chinmay only runs 96 m.
So the ratio of the speeds of Bhairav and Chinmay = 100/96 = 25 : 24.
Hence, we have B : A = 25 : 23 and B : C = 25 : 24.
So A : B : C = 23 : 25 : 24.
So when Chinmay covers 24 m,
Akshay only covers 23 m.
So if they race for 11/2miles = 2,400 m,
Chinmay will complete the race first
And the distance covered by Akshay = 2,300 m.
Therefore In other words, Chinmay would beat Akshay by 100 m
= 1 /16 mile
Question 5
Ram purchased a flat at Rs. 1 lakh and Prem purchased a plot of land worth Rs. 1.1 lakh. The respective annual rates at which the prices of the flat and the plot increased were 10% and 5%. After two years they exchanged their belongings and one paid the other the difference. Then
Ram paid Rs. 275 to Prem
Ram paid Rs. 475 to Prem
Ram paid Rs. 375 to Prem
Prem paid Rs. 475 to Ram
Question 5 Explanation: 
The price of flat after 2 years = (1)(1.10)2 = Rs. 1.21 lakh.
Therefore the price of land =(1.1)(1.05)2 = Rs. 1.21275 lakh.
Therefore,  price of the plot =  Rs. (1.21275 – 1.21) lakh
Which is  Rs. 275 more than that of the flat.
So , Ram will have to pay Prem this amount on exchanging their belongings.
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