Q1. A train covers a distance A and B in 45 minutes. If the speed is decreased by 5 km/hr, then it takes 48 minutes to cover the same distance. Find the distance between A and B (in km.) and the speed of a train?
(a) 60 km, 75 km/hr
(b) 60 km, 80 km/hr
(c) 40 km, 80 km/hr
(d) 70 km, 75 km/hr
Q2.A train covers a distance between A and B in 48 minutes. The another train having speed 6 km/hr. less than the first train covers the distance B to A in 60 minutes. Find the distance between A and B?
(a) 24 km
(b) 48 km
(c) 40 km
(d) 15 km
Q5. A book vendor sold a book at a loss of 20%. Had he sold it for Rs. 108 more, he would have earned a profit of 30%. Find the cost price of the book?
(a) Rs. 216
(b) Rs. 648
(c) Rs. 240
(d) Rs. 432
Q6. On mixing two classes A and B of students having average marks 25 and 40 respectively. The over all average obtained is 30. Find the ratio of the students in the class A and B.
(a) 2 : 1
(b) 5 : 8
(c) 5 : 6
(d) 3 : 4
Q7. At present the ratio of the age of Maya and Chhaya is 6 : 5 and fifteen years from now, the ratio will get changed to 9 : 8. Maya’s present age is
(a) 21 years
(b) 24 years
(c) 30 years
(d) 40 years
Q8. What must be added to each term of the ratio 7 : 11, so as to make it equal to 3 : 4?
(a) 8
(b) 7.5
(c) 6.5
(d) 5
Q9. The sum of three numbers is 68. If the ratio of the first to the second be 2 : 3 and that of the second to the third be 5 : 3, then the second number is
(a) 30
(b) 58
(c) 20
(d) 48
Q10. Two number are in the ratio 4 : 5 and their L.C.M. is 180. The smaller number is
(a) 9
(b) 15
(c) 36
(d) 45
Solutions
S1. Ans.(b)
Sol.
v1×t1=v2×t2
v×(45/60)=(v-5)×(48/60)
15v = 16v – 80
v = 80 km/h
D = v × t
=80×(45/60)
= 60 km
S2. Ans.(a)
Sol.
v1×t1=v2xt2
v×(48/60)=(v-6)×(60/60)
4v = 5v – 30
v = 30 km/h
D = v × t
=30×(48/60)
= 24 km
S3. Ans.(d)
Sol.
v1=7 (Let)
v2 = 9 (Let)
(l1/7)=4
l1=28
(l2/9)=6
l2=54
t=(28+54)/(7+9)
t=82/16
t=41/8
5 1/8
S4. Ans.(a)
Sol. To solve such questions, we keep 99 as it is in second part, but in part first, we convert all 9’s into zeros.
S5. Ans.(a)
Sol. (50/108)=(100/y)
y = Rs. 216
S8. Ans.(d)
Sol.(A/B)=(7/11) Given
Let x be added to both A & B
⇒(7+x)/(11+x)=3/4
Cross multiply the equation
28 + 4x = 33 + 3x
x = 5
S10. Ans.(c)
Sol.
A : B
4 : 5
4x : 5x
LCM = 4 × 5 × x = 20x
20x = 180
x = 9
∴ Smallest number is
= 4 × 9 = 36
Largest number is = 5 × 9 = 45
