Maths Quiz for 2016-17 Exams



Q1.Two equal sums were borrowed at 8% simple interest per annum for 2 years and 3 years respectively. The difference in the interest was Rs. 56/- The sums (in Rs.) borrowed were:
(a) Rs. 800/-
(b) Rs. 700/-
(c) Rs. 560/-
(d) Rs. 350/-
Sol. 
Let the borrowed = Rs. P
According to question, 56 = P * 8 * (3 – 2)/100
=> 5600/8 = P
=> P = Rs. 700/-

Q2. A  CD was sold at a profit of 12 ½ %. If It had been sold at a profit of 15%, It would have gained him Rs. 10/- more. The cost price of CD is (in Rs.)
(a) 450
(b) 500
(c) 400
(d) 550
Sol. 
Let cost price of CD = Rs. X
According to question,
X * 15/100 – x * 12 ½ * 1/100 = 10
=> 3x/20 – x/8 = 10
=> 6x – 5x/40 = 10
=> X = Rs. 400/-

Q3.If 3x – 1/4y = 6, then the value of 4x – 1/3y is :
(a) 2
(b) 4
(c) 6
(d) 8
Sol. 
3x – 1/4y = 6
4/3 (3x – 1/4y) = 4/3 * 6
(On multiplying by 4/3 both side)
4x – 1/3y =8

Q4. At present Ayushi is eight times her daughter’s age. Eight years from now, the ratio of the ages of Ayushi and her daughter will be 10 : 3 respectively. What is Ayushi’s present age ?
(a) 32 years
(b)  40 years
(c)  36 years
(d)  Can’t say
Sol.
 Let the age of Ayushi’s daughter be x. Then Ayushi’s age is 8x.
(8x + 8)/ (x + 8) = 10/3
x = 4
Ayushi present age = 8x = 32 years.

Q5. In how many different ways can 4 boys and 3 girls be arranged in a row such that all the boys stand together and all the girls stand together?
(a) 75
(b) 576
(c) 288
(d) 24
Sol. 
Required number of ways = 4! * 3! * 2! = 288.

Q6. X can do a piece of work in 20 days and Y can do it in 10 days. They started together, but after 6 days X leaves off. Y will do the rest work in
(a)  1 day
(b)  2 days
(c)  7/3 days
(d)  3 days
Sol. 
 (X + Y)’s 6 days’ work = 6 * (1/20 + 1/10) = 9/10
Remaining work = 1 – 9/10 = 1/10
1/10 work is done by Y in 10 * 1/10 = 1 day

Q7.The average wage of 500 workers was found to be Rs. 200. Later on, it was discovered that the wages of two workers were misread as 180 and 20 instead of 80 and 220. The correct average wage is :
(a) Rs. 200.10
(b) Rs. 200.20
(c) Rs. 200. 50
(d) Rs. 201.00
Sol.  
Total wages of 500 workers
= 500 * 200 = 100000
Now, according to question,
= (100000 – 180 – 20 + 80 + 220)/500
= 100100/500 = Rs. 200.20

Q8.The length of a train and that of a platform are equal. If  a speed of train 90 km/hr then train crosses the platform in one minute, then the length of the train (in metres) is :
(a) 500
(b) 600
(c) 750
(d) 900
Sol.
  Le the length of train be x metre
Speed = 90 km/hr
= (90 * 5) /18 meter/sec.
= 25 metre/sec.
so Distance covered in 60 sec.
= 25 * 60 = 1500 metres
Now, according to question.
2x = 1500
so x = 750 meter

Q9.A number when divided by the sum of 555 and 445, gives two times their difference as quotient and 30 as the remainder. The number is.
(a) 220030
(b) 22030
(c) 1220
(d) 1250
Sol. 
According to question,
Divisor = 555 + 445 = 1000
Dividend = ?
Quotient = (555 – 445) * 2
= 110 * 2 = 220
Remainder = 30
Dividend = (Divisor * Quotient) + Remainder
= (1000 * 220) + 30
= 220000 + 30 = 220030

Q10.A number of friends decided to go on a picnic and planned to spend Rs. 108 on eatables. Three of them however did not turn up. As a consequence each one of the remaining had to contribute Rs. 3 extra. The number of them who attended the picnic was:
(a) 15
(b) 12
(c) 9
(d) 6
Sol. 
 Let the number of friends be x.
so 108/(x – 3) – 108/x = 3
108 * 3 /x(x -3) = 3
=> x^2 – 3x = 108
=> x^2 – 12x + 9x – 108 = 0
=> x(x-12)  + 9 (x -12) = 0
(x – 12) (x + 9) = 0
X = 12
Number of friends who attended
= 12 – 3 = 9