# Mathematics Questions for CDS & AFCAT: 14th January (SOLUTIONS)

**Q1. 8% of the voters in an election did not cast their votes. In this election, there were only two candidates. The winner by obtaining 48% of the total votes defeated his contestant by 1200 votes. The total number of voters in the election was :**

(a) 20000

(b) 30000

(c) 35000

(d) 25000

**Q2. A train of length 200 m crosses another train of length 150 m, running on a parallel track in the opposite direction in 18 seconds. If the speed of train having length 150 m is 40 km/hr, then what is the speed (in km/hr) of the other train ?**

(a) 30

(b) 48

(c) 50

(d) 60

**Q3. What is the discount percentage offered on a test series having marked price Rs 2150 being sold at Rs 1892?**

(a) 12 %

(b) 13 %

(c) 14 %

(d) 16 %

**Q4. Rs 60500 is divided among W, X and Y such that W receives 2/9 as much as X and Y together and X receives 3/7 as much as W and Y together. What is the share of Y (in Rs)?**

(a) 29850

(b) 30120

(c) 31350

(d) 37250

**Q5. The average age of a dancing mob of 6 girls is x years. Four new girls having ages x – 2, x + 2, x + 4 and x + 6 joins the mob. What is the new average age (in years) of the mob?**

(a) x + 1

(b) x + 2

(c) 2.5x

(d) x + 2.5

**Q6. How much water (in litres) must be added to 80 litres solution of acid and water containing 10% acid, so that it becomes a 5% acid solution?**

(a) 10

(b) 20

(c) 40

(d) 80

(b) 5 : 4

(c) 8 : 7

(d) 7 : 8

**Q8. P and Q are the middle points of two chords (not diameters) AB and AC respectively of a circle with centre at a point O. the lines OP and OQ are produced to meet the circle respectively at the points R and S. T is any point on the major arc between the points R and S of the circle. If ∠BAC = 32°, ∠RTS = ?**

(a) 32°

(b) 74°

(c) 106°

(d) 64°

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