Mathmetics
ISBT Mathmetics for all banking PO,Clerk,IBPS PO,Railway,SSC,IAS,OAS Exams
Q1. | If the sides of a triangle measure 72, 75 and 21, what is the measure of its in radius? |
| 1) | 37.5 | 2) | 24 |
| 3) | 9 | 4) | 15 |
| 5) | None of these | ||
Explanation :
The sides of the triangle happen to be a Pythagorean triplet.
Hence, the triangle is a right angled triangle.
For a right angled triangle,the measure of in radius = (product of perpendicular sides) / (perimeter of triangle) = (7221) / (72 + 21 +75) = 1512 / 168 = 9
Q2. | The circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 36 ft long. What is the distance travelled by the cart, when the front wheel has done five more revolutions than the rear wheel ? |
| 1) | 20 ft | 2) | 25 ft |
| 3) | 750 ft | 4) | 900 ft |
| 5) | None of these | ||
Explanation :
The circumference of the front wheel is 30 ft and that of the rear wheel is 36 feet.
Let, the rear wheel make n revolutions. At this time, the front wheel should have made n+5 revolutions.
As both the wheels would have covered the same distance, n x 36 = (n+5) x 30
36 x n = 30n + 150
6n = 150
n = 25.
Thus, distance covered = 25 x 36 = 900 ft
Q3. | The ratio between the curved surface area and the total surface area is 2:3 and the total surface is 924 cm2. What is the volume of the cylinder? |
| 1) | 2156 cm3 | 2) | 2183 cm3 |
| 3) | 2492 cm3 | 4) | 2592 cm3 |
| 5) | None of these | ||
Explanation :
Total surface area = 924 cm2
Then, the curved surface area = (924 /3) ×2 = 308 ×2 616 cm2
Area of the base = (924- 616)/ 2 = 154cm2.
Let, the radius of base = r and pie r2 = 154 cm2
So, r2 = (154× 7) / 22 = 49
or r = 7 cm.
Then, 2pie r = 2× (22/ 7)× 7 44 cm.
Hence, surface area = 2pie rh = 616 cm2
Or, 2× (22 /7)× 7 h= 616
or h = (616/ 44)
Volume = pie r2h = 154 × (616 /44) cm3 = 2156 cm3
Q4. | A solid wooden toy is in the shape of a right circular cone mounted on the base of a hemisphere. If the radius of the hemisphere is 4.2 cm and the total height of the toy is 10.2 cm, find the volume of the wood needed to construct another such toy. |
| 1) | 104 cm3 | 2) | 162 cm3 |
| 3) | 427 cm3 | 4) | 266 cm3 |
| 5) | None of these | ||
Explanation :
The total volume of the wood is the sum of the volumes of the hemisphere and the right circular cone.
(â…“ x 22/7 x 4.2 x 4.2 x 10.2 ) + ( â…” x 22/7 x 4.2 x4.2 x4.2)
=22 x 0.84 x 14.4 =266.112 cm^3
Q5. | A mixture of 450 ml contains milk and water in the ratio 2 : 1. How much more water must be added to make the new ratio of milk and water 4 : 5 ? |
| 1) | 215 ml | 2) | 220 ml |
| 3) | 225 ml | 4) | 235 ml |
| 5) | None of these | ||
Explanation :
Old Ratio: milk: water = (2 : 1)
New Ratio:milk: water= (4 : 5)
Multiply the Old Ratio by 2 to equalise milk, so the milk parts match (4).
- Balanced Milk: (2:1) became (4:2) (Total parts = (6))
- Found the Value: (450 ml /6 = 75 ml per part
- Multiplied the Difference: Water went from (2 to 5) i.e (3parts), so 3 x 75 =225ml
Q6. | The circumference of the back-side wheel of a vehicle is 1 m greater than that of. front-side wheel. To travel 600 m the front wheel rotates 30 times more than the back wheel. what should be the circumference of the front wheel ? |
| 1) | 5 m. | 2) | 2 m. |
| 3) | 3 m. | 4) | 4m |
| 5) | None of thes | ||
Q7. | The circumference of the back-side wheel of a vehicle is 1 m greater than that of. front-side wheel. To travel 600 m the front wheel rotates 30 times more than the back wheel. what should be the circumference of the front wheel ? |
| 1) | 5 m. | 2) | 2 m. |
| 3) | 3 m. | 4) | 4m |
| 5) | None of thes | ||
Explanation :
Let the circumference of front wheel be x metres.
Then, Circumference of rear wheel = (x - 1) metres
∴600/x−600/(x+1)=30
⇒1/x(x+1)=1/20
⇒x(x−1)=20
⇒(x2+x−20)=0
⇒(x+5)(x−4)=0⇒x=4m
Q8. | If 40 men can build a wall 300 m long in 12 days working 6; hours a day, how long will 30 men take to build a similar wall 200 m long working 8 hours a day ? |
| 1) | 4½ days | 2) | 10½ days |
| 3) | 8 days | 4) | 11 days |
| 5) | None of these | ||
Explanation :
Sol. M1D1W2T1 = M2D2W1T2
or D2 = (40 x 12 x 200 x 6)/ (30 x 300 x 8 ) = 8 days
Q9. | Three men or eight boys can do a piece of work in 17 days. How many days will two men and six boys together take to finish the same work ? |
| 1) | 9 days | 2) | 11 days |
| 3) | 14 days | 4) | 12 days |
| 5) | None of these | ||
Explanation :
3 men = 8 boys
2 men =(8x2)/3 = 16/3 boys.
(2 men + 6 boys) =[(16/3 )+6] boys
= (34/3) boys
Given, 8 boys can complete the work in 17 days
(34/3 boys can complete the work in x days
34/3 : 8 = 17 : x
x =(17x8x3)/34 = 12 days
Q10. | In a certain store, the profit is 260% of the cost. If the cost increases by 20% but the selling price remains constant, approximately what percentage of the selling price is the profit? |
| 1) | 33-1/3% | 2) | 40% |
| 3) | 54% | 4) | 66-2/3% |
| 5) | None of these | ||
Explanation :
