 # Sample Aptitude Questions of ITC

1. If √1+x/961=32/31, then the value of x is
1. 63
2. 61
3. 65
4. 64

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

⇒ The sum of two odd number is even. The same is the case with their product.
∴ a + b + 2ab = Even number
1. 216-1 is divisible by
1. 11
2. 13
3. 17
4. 19

216 - 1 = (28)2 -1
= (28 + l) (28 - l)
= (256 + 1) (256 - 1)
= 257 × 255 which is exactly divisible by 17.
2. The single discount equal to three consecutive discounts of 10%, 12% and 5% is
1. 26.27%
2. 24.76%
3. 9%
4. 11%

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%
3. If x : y = 5 : 6, then (3x2 - 2y2): (y2 - x2) is
1. 7:6
2. 11:3
3. 3:11
4. 6:7

x/y= 5/6
⇒ 3x2 - 2y2 /y2 - x2 =3 .( x2/y2 )-2 /1-(x2/y2)
⇒ 3*25/36 -2 /1 -25/36 =75 -72 /36 -25 = 3 /11
4. 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
1. 8
2. 10
3. 12
4. 15

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.
5. 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. 1:2
2. 3:5
3. 3:4
4. 2:5

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
6. 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
1. 8
2. 6
3. 4
4. 2

Let the numbers be 2x and 3x.
∴ (2x+4)/(3x+4) = 5/7
⇒ x = 28 – 20 = 8 = Required difference
7. 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
1. Rs. 12,000
2. Rs. 24,000
3. Rs. 30,000
4. Rs. 60,000

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
8. 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?
1. 15
2. 17
3. 19