**If √1+x/961=32/31, then the value of x is**- 63
- 61
- 65
- 64

Answer : Option A.

√1+ x/961= (32/31)^{2},

Squaring both sides,

⇒ 1+ x/961 = (32/31)2 = 1024/961Therefore, x/961 = 1024/961 -1 = 1024-961 /961 = 63/961⇒ x = 63**a and b are odd numbers, then which of the following is even?**- a + b + ab
- a + b-1
- a + b + 1
- a + b + 2ab

Answer : Option D.

⇒ The sum of two odd number is even. The same is the case with their product.

∴ a + b + 2ab = Even number

**2**^{16}-1 is divisible by- 11
- 13
- 17
- 19

Answer : Option C.

2^{16}- 1 = (2^{8})^{2}-1

= (2^{8}+ l) (2^{8}- l)

= (256 + 1) (256 - 1)

= 257 × 255 which is exactly divisible by 17.**The single discount equal to three consecutive discounts of 10%, 12% and 5% is**- 26.27%
- 24.76%
- 9%
- 11%

Answer : Option B.

Single equivalent discount for 10% and 12%.

⇒ (12 -10 -12*10 /100)% = 20.8%

Single equivalent discount for 20.8% and 5%.

⇒(20.8 -5 -20.8*5/100)% = 20.8%

= 24.76%**If x : y = 5 : 6, then (3x**^{2}- 2y^{2}): (y^{2}- x^{2}) is- 7:6
- 11:3
- 3:11
- 6:7

Answer : Option C.

x/y= 5/6

⇒ 3x^{2}- 2y^{2}/y^{2}- x^{2}=3 .( x^{2}/y^{2})-2 /1-(x^{2}/y^{2})

⇒ 3*25/36 -2 /1 -25/36 =75 -72 /36 -25 = 3 /11ITC Preparation Links- Sample Aptitude Questions of ITC
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**An alloy contains copper, zinc and nickel in the ratio of 5 : 3 : 2. The quantity of nickel in kg that must be added to 100 kg of this alloy to have the new ratio 5 : 3 : 3 is**- 8
- 10
- 12
- 15

Answer : Option B.

Let x kg of nickel be mixed.

20+x/100+x= 3/11

⇒ 220 + 11x = 300 + 3x

⇒ 11x - 3x = 300-220

⇒ 8x = 80 ⇒ x = 10 kg.**The ratio of the ages of Ram and Rahim 10 years ago was 1 : 3. The ratio of their ages five years hence will be 2 : 3. Then the ratio of their present ages is**- 1:2
- 3:5
- 3:4
- 2:5

Answer : Option B.

Let the ages of Ram and Rahim 10 years ago be x and 3x years respectively.

After 5 years from now,

x+15/3x+15=2/3

⇒ 6x + 30 = 3x + 45

⇒ 3x = 45-30 = 15

⇒ x = 5

∴ Radio of their present ages

= (x+ 10) : (3x + 10)

= 15 : 25 = 3 : 5**The ratio between two numbers is 2 : 3. If each number is increased by 4, the ratio between them becomes 5 : 7. The difference between the numbers is**- 8
- 6
- 4
- 2

Answer : Option A.

Let the numbers be 2x and 3x.

∴ (2x+4)/(3x+4) = 5/7

⇒ x = 28 – 20 = 8 = Required difference**Monthly incomes of A and B are in the ratio of 4 : 3 and their expenses bear the ratio 3:2. Each of them saves Rs. 6,000 at the end of the month, then the monthly income of A is**- Rs. 12,000
- Rs. 24,000
- Rs. 30,000
- Rs. 60,000

Answer : Option B.

Let the monthly incomes of A and B be Rs. 4x and Rs. 3x respectively and their expenditures be Rs. 3y and Rs. 2y respectively.

∴ 4x – 3y = 6000 and 3x – 2y = 6000

⇒ 4x – 3y = 3x – 2y ⇒ x = y ∴ 4x – 3y = 6000

⇒ x = 6000

⇒ A’s monthly income = 4x = Rs. 24000**The average of three consecutive odd numbers is 12 more than one third of the first of these numbers. What is the last of the three numbers?**- 15
- 17
- 19
- Data inadequate

Answer : Option C.

If the smallest number be x, then

X/3+12=x+2=x+36=3x+6

⇒ 3x – x = 36 – 6 ⇒ 2x = 30 ⇒ x = 15

∴ Third number = 15 + 4 = 19