Page 171 - ICSE Math 8

Each side is increased by 10 cm.
\ New sides are a + 10, b + 10, c + 10

\ Perimeter of new triangle = (a + 10) + (b + 10) + (c + 10)
= a + b + c + 30 = x + 30 ...(from 1)
Perimeterofnew triangle 5
According to the question, =
Perimeterofgiven triangle 4
x + 30 5
fi = (Cross-multiply)
x 4
fi 5x = 4(x + 30) fi 5x = 4x + 120
fi 5x – 4x = 120 fi x = 120 (Transposing 4x to LHS)
\ Perimeter of the given triangle is 120 cm.

EXERCISE 15.4

1. The sum of two numbers is 70. Their difference is 16. Find the numbers.
2. The difference between two positive integers is 36. The quotient when one integer is divided by the other
is 4. Find the two integers.
3. Two numbers are such that the first number is 5 times the second number. If 10 is added to both the
numbers, the first number becomes 3 times the second number. Find the two numbers.
4. Divide 60 into two parts, such that 3 times the smaller part may exceed 100 by as much as
9 times the bigger falls short of 200.
5. A 2-digit number is such that the sum of its digits is 8. If 54 is subtracted from the number, its digits are
reversed. Find the number.
6. The difference between the squares of two consecutive numbers is 31. Find the numbers.
7. The numerator of a fraction is 8 less than the denominator. If the numerator is increased by 17 and the
3
denominator is decreased by 1, the new fraction obtained is . Find the fraction.
2
8. The digit at the tens place of a 2-digit number is 3 times the digit at the units place. If the digits are
reversed, the new number will be 36 less than the original number. Find the number.

9. Manav has a small box with ` 740 in coins of denominations ` 1, ` 2 and ` 5. If the number of coins of
denomination of ` 2 are 3 times the number of coins of denomination of ` 1 and the number of coins
of denomination of ` 5 are twice the number of coins of ` 2, how many coins of each denomination does
Manav has?
10. The organizers of a story writing competition decided that the winner in the competition will get a prize
of ` 200 and a participant who participates and does not win will get a prize of ` 50. The total prize money
distributed is ` 6,000. Find the number of winners, if the total number of participants is 60.
1
11. Sonika went for shopping. She spent of the amount she had on buying dresses for her children
2
1
and gave ` 2 to a beggar. She spent of what was left on lunch and gave ` 10 as tip. She spent
2
1 of the remaining amount for buying stationary for her children and spent ` 6 as bus fare.
2
When they reached home, Sonika had ` 20 left in her purse. How much money did she take for shopping?
12. Aishwarya is twice as old as Karishma. If six years are subtracted from Karishma’s age and four years are
added to Aishwarya’s age, then Aishwarya’s age will be 4 times Karishma’s age. How old were they two
years ago?

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