# Sample Aptitude Questions of Cummins

1. 1. A mixture contains wine and water in the ratio 3 : 2 and another mixture contains them in the ratio 4: 5. How many liters of the latter must be mixed with 3litres of the former so that the resultant mixture may contain equal quantities of wine and water?
1. 1 2/3 litre
2. 2/5 litre
3. 3 3/4 litre
4. 4 1/2 litre
5. None of these

By applying allegation and mixture So we got ratio of two mixture = 5:9
It means 5 unit = 3 liters
We get 9 unit = 3/5 ×9 = 27/5 liters
1. 2. A trader sells two bullocks for Rs. 8,400 each, neither losing nor gaining in total. If he sold one of the bullocks at a gain of 20%, the other is sold at a loss of
1. 20%
2. 18 2/9%
3. 14 2/7%
4. 21%
5. None of these

A trader sells two bullocks for Rs. 8,400 each, neither losing nor gaining in total.
As he sold one bullocks at a gain of 20%, it means 120% of C.P = 8400
We get C.P of one bullocks = 7000
So gains on one bullocks = Rs 1400
Other bullocks is sold at lose and there is neither losing nor gaining in total
So loss on 2nd bullocks = 1400/7000×100 =20%
2. Two trains, A and B, start from stations X and Y towards each other, they take 4 hours 48 minutes and 3 hours 20 minutes to reach Y and X respectively after they meet if train A is moving at 45 km/hr., then the speed of the train B is
1. 60 km/hr
2. 64.8 km/hr
3. 54 km/hr
4. 37.5 km/hr
5. None of these

Speed1 : Speed2 = √Time2 : √Time1
45km/h :speed2 = √10/3 : √24/5
We get speed2 = 54km/hr
3. Out of his total income, Mr. Kapoor spends 20% on house rent and 70% of the rest on house hold expenses. If he saves Rs 1,800 what is his total income (in rupees)?
1. Rs 7,800
2. Rs 7,000
3. Rs 8,000
4. Rs 7,500
5. None of these

Let the total income of Mr. Kapoor be 100 units.
As Mr. Kapoor spends 20% on house rent and 70% of the rest on house hold expenses.
So he spends 76% of his income.
It means 24 unit income = Rs 1,800
Total income = 1,800/24 ×100 = Rs. 7500
4. A can do a piece of work in 8 days which B can destroy in 3 days. A has worked for 6 days, during the last 2 days of which B has been destroying. How many days must A now work alone to complete the work?
1. 7 days
2. 7 2/3 days
3. 7 1/3 days
4. 8 days
5. None of these

A can do a piece of work in 8days which B can destroy in 3 days.
So let the total work be 24 units.
So unit contributed by A and B in one day is 3 units and -8 units respectively .
A has worked for 6 days, during the last 2 days of which B has been destroying.
So total units completed in 6 days = 6×3 + 2× (-8) = 2 units.
So remaining 22 units is done by A alone with efficiency of 3 units per day.
So number of days required to complete the work = 22/3 days
5. A garrison of 750 men has provisions for 20 weeks. If at the end of 4 weeks, they are re-inforced by 450 men, how long will the provision last?
1. 8 weeks
2. 12 weeks
3. 14 weeks
4. 15 weeks
5. 10 weeks

750 * 20 = 750 * 4 + 1200 * W  => W = 10 weeks
6. Bill, Simon, and John are brothers, given Simon is the eldest. Bill is as many years younger than one brother as he is older than the other. Simon is 7 years younger than twice the age of John. John is 5 years older than half the age of Bill. What is the sum of the ages of Bill, Simon and John?
1. 12
2. 24
3. 48
4. Can’t say

S – B = B – J J = B/2 + 5. S = 2J – 7.
S = B + 10 – 7 = B + 3.
J = + 5. 2S = B + 10. + 5 + B + 3 = 2B. = 8. B = 16, S = 19, J = 13. So B + S + J = 16 + 19 + 13 =48.
7. The cost price of item B is Rs. 150/- more than the cost price of item A, Item A was sold at a profit of 10% and Item B was sold at a loss of 20%. If the respective ratio of selling price of items A and B is 11:12, what is the cost price of item B?
1. Rs. 450/-
2. Rs. 420/-
3. Rs. 400/-
4. Rs. 350/-
5. Rs. 480/-

Let us assume cost price of A= X
So that Cost price of B= X+150.
SP of A= X*1.1
SP of B=(X+150)*0.8
Given that
SPA: SPB
11:12
So that 1.1X/(X+150)*0.8= 11/12
X=300
CP of B= 300+150=450
8. The number of ways in which 7 boys and 8 girls can be seated in a row so that they are alternate
1. 203121800
2. 29030400
3. 3628800
4. 203212800
5. 3628800