| Exercise-XIII |
| 1. |
The average weight of 10 oarsmen in a boat is increased by 1.5 pounds when one of the crew, who weighs 58 pounds is replaced by a new man. Find the weight of new man ? |
| Sol: |
Total weight increased |
= |
10 × 1.5 pounds |
| |
|
= |
15 pounds |
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weight of new man |
= |
(58 + 15) pounds |
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|
= |
73 pounds |
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 |
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| 2. |
10 sheep and 5 pigs were bought for $ 6000. If the average price of a sheep be $ 450, find the average price of a pig |
| Sol: |
Total price of 10 sheep |
= |
10 × 450 |
| |
|
= |
$ 4500 |
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Total price of 5 pigs |
= |
$ 6000 – $ 4500 |
| |
|
= |
$ 1500 |
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Average price of a pig |
= |
 |
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|
= |
$ 300 |
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 |
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| 3. |
 of x is 900 what is the value of  of x ? |
| Sol: |
 |
| |
 × x |
= |
900 |
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 |
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x |
= |
2400 |
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of 2400 |
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 |
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 |
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| 4. |
x, y are natural numbers if x2 + y2 = 80 and (x – y)2 = 36, what is the value of xy ? |
| Sol: |
x2 + y2 – 2xy |
= |
(x – y)2 |
| |
80 – 2xy |
= |
36 |
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80 – 36 |
= |
2xy |
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2xy |
= |
44 |
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xy |
= |
22 |
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 |
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| 5. |
If 1 is added to the denominator of a fraction  the fraction becomes  . If 1 is added to the numerator, the fraction becomes 1 what is the fraction |
| Sol: |
 |
= |
|
| |
2x |
= |
y + 1 |
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2x – y |
= |
1 ––– (1) |
| |
 |
= |
1 |
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x + 1 |
= |
y |
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x – y |
= |
– 1 ––– (2) |
| |
subtract 2 from 1 |
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 |
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x + 1 |
= |
y |
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2 + 1 |
= |
y |
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y |
= |
3 |
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|
= |
 |
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 |
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| 6. |
The sum of three numbers is 132. If the first number be twice the second and third number be one third of the first, then the second number is |
| Sol: |
Let 2nd number be x |
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1st number be 2x |
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3rd number be  × 2x |
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 |
= |
132 |
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 |
= |
132 |
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11x |
= |
132 × 3 |
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 |
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2nd number = x |
= |
36 |
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 |
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|
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| 7. |
If a + b = 45, b + c = 55, c + 3a = 90 what is the value of the third number ? |
| Sol: |
 |
| |
a + 10 |
= |
c ––– (3) |
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c + 3a |
= |
90 ––– (4) |
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c |
= |
90 – 3a |
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c |
= |
10 + a |
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90 – 3a |
= |
10 + a |
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90 – 10 |
= |
3a + a |
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4a |
= |
80 |
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a |
= |
20 |
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c |
= |
10 + a |
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|
= |
10 + 20 |
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c |
= |
30 |
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 |
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|
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| 8. |
A circular wire of radius 42" is cut and bent in the form of a rectangle whose sides are in the ratio 6 : 5. The smaller side of the rectangle is |
| Sol: |
circumference of circle |
= |
perimeter of rectangle |
| |
2πR |
= |
2(L + B) |
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L : B |
= |
6 : 5 |
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Let L = 6x, B = 5x |
| |
 |
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264 |
= |
22x |
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x |
= |
12 |
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B |
= |
5x |
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|
= |
5 × 12 |
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|
= |
60" |
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 |
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|
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| 9. |
The number of rounds that a wheel of diameter  m will make in going 4 km (1 km = 1000 metres) |
| Sol: |
Number of rounds |
= |
 |
| |
|
= |
 |
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 |
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|
= |
 |
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|
= |
2000 |
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 |
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| 10. |
The area of the circle inscribed in an equilateral triangle is 462 sqinches. The sides of the triangle is |
| Sol: |
πr2 |
= |
462 |
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 |
| |
r2 |
= |
147 |
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r |
= |
 |
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|
= |
 |
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r |
= |
7√3 |
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radius of incircle |
= |
× height of triangle |
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7√3 |
= |
× height of the triangle |
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height of the triangle |
= |
21√3 |
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height of triangle |
= |
 side |
| |
 |
= |
side |
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side |
= |
42" |
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 |
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| 11. |
a, b, c, d are four numbers such that a – s = b + 6 = c + 9 = d – 1. What is the value of a – d : b – c |
| Sol: |
a – 5 |
= |
d – 1 |
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a – d |
= |
5 – 1 |
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a – d |
= |
4 |
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b + 6 |
= |
c + 9 |
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b – c |
= |
9 – 6 |
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b – c |
= |
3 |
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a – d : b – c |
= |
4 : 3 |
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 |
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 |
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| 12. |
a > b, b < c, c > d If a = b + 2, b = c – 3, c = d + 4 what is the value of (a – d)2 + (a – d) |
| Sol: |
a |
= |
b + 2 |
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b |
= |
c – 3 |
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a |
= |
c – 3 + 2 |
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a |
= |
c – 1 |
| |
a |
= |
d + 4 – 1 |
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a |
= |
d + 3 |
| |
a – d |
= |
3 |
| |
(a – d)2 + (a – d) |
= |
(3)2 + 3 |
| |
|
= |
12 |
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 |
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| 13. |
The perimeter of rectangle is 64" and the length is 18". What is the area of ΔPOQ ? |
| Sol: |
2(L + B) |
= |
64" |
| |
2(18" + B) |
= |
64" |
| |
(18" + B) |
= |
32" |
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QR |
= |
B = 14" |
| |
OX |
= |
× QR |
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|
= |
× 14" |
| |
|
= |
7" |
| |
Area of ΔPOQ |
= |
× QP × OX |
| |
 |
| |
|
= |
63" sqinches |
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 |
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SAT Math