**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 2/3 litre
- 2/5 litre
- 3 3/4 litre
- 4 1/2 litre
- None of these

Answer : Option E.

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

**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**- 20%
- 18 2/9%
- 14 2/7%
- 21%
- None of these

Answer : Option A.

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%**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**- 60 km/hr
- 64.8 km/hr
- 54 km/hr
- 37.5 km/hr
- None of these

Answer : Option C.

Speed1 : Speed2 = √Time2 : √Time1

45km/h :speed2 = √10/3 : √24/5

We get speed2 = 54km/hr**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)?**- Rs 7,800
- Rs 7,000
- Rs 8,000
- Rs 7,500
- None of these

Answer : Option E.

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**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?**- 7 days
- 7 2/3 days
- 7 1/3 days
- 8 days
- None of these

Answer : Option C.

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 daysCummins Preparation Links- Sample Aptitude Questions of Cummins
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**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?**- 8 weeks
- 12 weeks
- 14 weeks
- 15 weeks
- 10 weeks

Answer : Option E.

750 * 20 = 750 * 4 + 1200 * W => W = 10 weeks**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?**- 12
- 24
- 48
- Can’t say

Answer : Option C.

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.**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?**- Rs. 450/-
- Rs. 420/-
- Rs. 400/-
- Rs. 350/-
- Rs. 480/-

Answer : Option A.

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

Answer is 450.**The number of ways in which 7 boys and 8 girls can be seated in a row so that they are alternate**- 203121800
- 29030400
- 3628800
- 203212800
- 3628800

Answer : Option D.

Reqd. number of ways = 7! × 8! = 203212800.**There are 13 married couples, 5 single men and 7 single women in a party. Every man shakes hand with every woman once, but no one shakes hand with his wife. How many handshakes took place in the party?**- 247
- 347
- 360
- 191
- 100

Answer : Option B.

Any single man will have = 13 + 7 = 20 options.

Total number of handshakes by single men = 20 × 5= 100. Any married man will have 12 + 7 = 19 options. Total number of handshakes by married men = 19 × 13 = 247. Total number = 247 + 100 = 347.