1.In a question on division, the divisor is 7 times the quotient and 3 times the remainder. If the remainder is 28, then the dividend is
(a) 588
(b) 784
(c) 823
(d) 1036
2.The greatest whole number, by which the expression n^4 + 6n^3 + 11n^2 + 6n + 24 is divisible for every natural number n, is
(a) 6
(b) 24
(c) 12
(d) 48
3.A certain distance is covered by a vehicle at a certain speed. If half of this distance is covered by another vehicle in double the time, the ratio of the speeds of the two vehicles is
(a) 1 : 4
(b) 1 : 2
(c) 2 : 1
(d) 4 : 1
4.The ratio of lengths of two trains is 5 : 3 and the ratio of their speeds is 6 : 5. The ratio of times taken by them to cross a pole is
(a) 5 : 6
(b) 11 : 8
(c) 25 : 18
(d) 27 : 16
5.If the average weight of 6 students is 50 kg; that of 2 students is 51 kg; and that of 2 students is 55 kg; then the average weight of all students is
(a) 61 kg
(b) 51.5 kg
(c) 52 kg
(d) 51.2 kg
6.From a class of 24 boys, a boy, aged 10 years. Leaves the class and in his place a new boy is admitted. As a result, the average age of the class is increased by 2 months. What is the age of the new boy?
(a) 12 years
(b) 15 years
(c) 14 years
(d) 13 years
7.In a village, each of the 60% of families has a cow: each of the 30% of families has a buffalo and each of the 15% of families hAs both a cow and buffalo. In all there are 96 families in the village. How many families do not have a cow or a buffalo?
(a) 20
(b) 24
(c) 26
(d) 28
8.The price of sugar is increased by 20%. As a result, a family has decreased its consumption by 20%. The expenditure of the family on sugar is decreased by
(a) 0 %
(b) 2.5%
(c) 4%
(d) 5%
9.The ratio of the present ages of Rahul and Rashmi is 2 : 1. The ratio of their ages after 30 years will be 7 : 6. What is the present age of Rahul?
(a) 6 years
(b) 10 years
(c) 12 years
(d) 20 years
10.The price of sugar is increased by 20%. If the expenditure on sugar has to be kept the same as earlier, the ratio between the reduction in
consumption and the original consumption is
(a) 1 : 3
(b) 1 : 4
(c) 1 : 6
(d) 1 : 5
ANSWERS AND SOLUTION:
1.(d) Let the quotient be Q and the remainder by R. Then
Divisor = 7Q = 3 R
SO Q = 3/7 R = 3/7 * 28 = 12
so Divisor = 7Q = 7 * 12 = 84
so Dividend = Divisor * Quotient +Remainder = 84 * 12 + 28
= 1008 + 28 = 1036
2.(d) For n = 1
n^4 + 6n^3 + 11n^2 + 6n + 24
= 1 + 6 + 11 + 6 + 24 = 48
For, n = 2
n^4 + 6n^3 + 11n^2 + 6n + 24
= 16 + 48 + 44 + 12 + 24
= 144 which is divisible by 48.
Clearly, 48 is the required number.
3.(d) Time and speed bear inverse ratio.
4.(c) Required ratio
= 5/6 : 3/5 = (30 * 5)/6 : (30 * 3)/5
= 25 : 18
5.(d) Required average weight
(50 * 6 + 51 * 2 + 55 * 2) /10
= (300 + 102 + 110)/10 = 512/10
= 51.2 kg
6.(c) Total age increased
= 2 * 24 = 48 months = 4 years
so Age of the new boy
= 10 + 4 = 14 years
7.(b) Per cent of families having either a cow or a buffalo or both
= 60 + 30 – 15 = 75
It means 25 per cent of families do not have a cow or a buffalo.
so Required number of families
= 25% of 96 = 96 * 25/100 = 24
8(c) Effective decrease
= (20 * 20)/100 = 4%
9.(c) Let the present ages of Rahul and Rashmi be 2x and x years respectively.
After 30 years.
(2x+30)/(x+30 )=7/6
=> 12x + 180 = 7x + 210
=> 12x -7x = 210 – 180
=> 5x = 30
=> x = 30/5 = 6
so Rahul’s present age
= 2x = 2 * 6 = 12 years
10.(c) The raised price = 120/100 of the former price
so The householder must now consume 100/120 of the original amount
so The reduction in consumption
= (1 – 100/120) of the original consumption = 1/6 of the original consumption
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