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Arithmetic : Level 2 Test-6

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Question 1
There are 2 bottles containing a mixture of wine, water and alcohol. The first bottle contains wine, water and alcohol in the ratio 3 : 5 : 2. The second bottle contains water and wine in the ratio 5 : 4. 1 L of the first and 2 L of the second are mixed together. What fraction of the mixture is alcohol?
1/15 L
6/13 L
2/15 L
6/19 L
Question 1 Explanation: 
Given that the Quantity of alcohol in 1 L mixture of first bottle = 2/10 x 1=1/5 l
Now second bottle does not contain any alcohol so the required quantity will be 1/3 x 1/5 = 1/15
Question 2
Mohan and Puran are running towards each other, each one from his own house. Mohan can reach Puran's house in 25 min of running, which is half the time it takes Puran to reach Mohan's house. If the two started to run at the same time, how much more time will it take Puran to reach the middle than  Mohan?
35 min
25 min
12.5 min
50 min
Question 2 Explanation: 
Mohan can reach Puran's house in 25 min of running,
which is half the time it takes Puran to reach Mohan's house.
Therefore it is simple that Mohan will be on the half way in 12.5 minutes and Puran can reach to the half way in 25 minutes,
so the time required for Puran to reach in the middle is 25- 12.5 = 12.5 mins.
Question 3
Two cars A and B are travelling on the same road towards each other. If car A is travelling at a speed of 120 km/h and car B is travelling 15% slower than A, how much time will it take the cars to meet, if the initial distance between the two is 668.4 km and car A started to drive one and a half hour before car B started?
2 h and 12 min
2 h
1 hour and 30 min
3 h and 15 min
Question 3 Explanation: 
Speed of the car A = 120km/h
Car B is travelling at 15% slower than the A therefore the speed of the car B = 102km/h
Distance travelled by the car in one and half hour = 180 km
Distance remaining between both now = (668.4 – 180) km
Now relative speed will be (120 + 102) km/h
And therefore the required time will be (668.4 – 180) km/h / (120 + 102) = 2.2 h
Question 4
A train travelling at 100 km/h overtakes a motorbike travelling at 64 km/h in 40 s. What is the length of the train in metres taking length of motorcycle negligible?
400 m
1822 m
1777 m
1111 m
Question 4 Explanation: 
Let the speed of the train = s km/h
Since train is overtaking, the motorbike so both are raveling in the same
directions and therefore the length of the train will be
40 x (100 – 64) x 5/18 (after converting)
= 400 m
Question 5
Working together, Asha and Sudha can complete an assigned task in 20 days. However, if Asha worked alone and complete half the work and then Sudha takes over the task and completes the second half of the task, the task will be completed in 45 days. How long will Asha take to complete the task if she worked alone? Assume that Sudha is more efficient than Asha.
60 days
30 days
25 days
65 days
Question 5 Explanation: 
Let Asha can complete the work in p days
Let Sudha can complete the work in q days
We know that they can complete the wok in 20 days
i.e. 1/p + 1/q = 1/20 ………………………. (i)
and p/2 + q/2 = 45 ………………………..(ii)
p + q = 90………………………………………….(iii)
From equation (i) and (iii)
pq = 1800
Now make the pairs from option whose sum would be 90 and multiplication would be 1800
So there is only one pair i.e. 60 x 30
And we know that Sudha is more efficient than the Asha, so Asha can do the work in 60 days.
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