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1. Find two numbers whose sum shall be triple of their difference and also less than 100 by the smaller of the two.

2. There is a certain fraction which, if I be added to its numerator, becomes; but if I be added to its denominator, it becomes : what is the fraction?

3. The sum of the two digits of a certain number is six times their difference, and the number itself exceeds six times their sum by 3: find it.

4. If the digits in a certain number consisting of two figures be inverted, the sum of the two numbers will be 121, and the difference between them will be 9: find the number.

5. If a father was four times as old as his son seven years ago, and will be twice as old as his son in seven years more, what is the present age of each?

6. A man sold 8 horses and 10 cows for 350%, and 10 horses and 8 cows for 370l.: what was the price of each?

7. A farmer sells 19 horses and 7 cows for 547%, and 6 horses and 31 cows for the same sum: what was the price of each?

8. From the termini of a railway a miles long two trains are despatched, one b minutes later than the other; at c minutes after the first train has started they meet half-way if the speeds of the trains be interchanged, at what point will they meet?

9. An eleven at cricket scored 58; two scored nothing, seven scored 30 between them, and the difference between the two principal scores was 10: find what each of these two scores amounted to.

10. What fraction is that, to the numerator of which if I be added, its value will be ; but if I be added to the denominator, its value will be ?

11. A man bought 3 horses and 5 cows, and gave the same sum for the 3 horses as for the 5 cows; if he had bought 4 horses and 10 cows, his outlay would have been 120%. more: find what his outlay was.

12. Two numbers consist of the same two digits, but in an inverse order; the sum of the numbers is 55, and their difference is 27: find them.

13. A number consists of three digits, the right-hand one being o; if the left-hand and the middle digits be interchanged, the number will be diminished by 180; if the left-hand digit be halved, and the middle and righthand digits be interchanged, the number will be diminished by 454: find the number.

14. A, B, C, and D have 290l. between them: A has twice as much as C, and B three times as much as D; also C and D together have 50%. less than A: find how much each has.

15. The difference between two numbers is one-fourth of their sum; and the half of the greater, diminished by 7, is equal to one-fifth of the less, increased by 21: find the numbers.

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(8) ex-e*+ I.

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